Configure ConnectionString for connect from different domain in SQL Server 2008

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C#2.0

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I want to connect with MS-SQL SERVER 2008's Database from a different domain.

The ip of MS-SQL Server 2008 is: 192.168.55.33
Server Name: BDC\SQLEXPRESS
DataBase Name: DMNG
Login: sa
Password: samsung001

My App.config is:

<?xml version="1.0" encoding="utf-8" ?>
<configuration>
  <appSettings>
    <!--   User application and configured property settings go here.-->
    <!--   Example: <add key="settingName" value="settingValue"/> -->
    <add key="SqlConnectionString" value="Data Source=192.168.55.33\BDC\SQLEXPRESS;Initial Catalog=DMNG;UID=sa;Password=Support2010; Integrated Security=True;"/>

  </appSettings>
</configuration>

My SqlConnectoin.cs is:

using System;
using System.Collections.Generic;
using System.Text;
using System.Data;
using System.Data.SqlClient;
using System.Configuration;
using System.IO;

namespace DMNG_Management
{
    public class SqlDBAccess
    {
        #region Variables
        private string _connectionString;
        private string _databaseName;
        private string _serverName;
        private string _userName;
        private string _password;
        public SqlConnection connection = new SqlConnection();
        public SqlCommand command = new SqlCommand();
        private SqlDataAdapter adapter = new SqlDataAdapter();
        private SqlDataReader reader;
        public DataSet dataSet = new DataSet();
        private DataTable dataTable = new DataTable();
        private SqlCommandBuilder commandBld = new SqlCommandBuilder();
        public SqlTransaction transaction = null;
        private Object obj;
        #endregion
        #region Properties
        public string ConnectionString
        {
            set
            {
                _connectionString = value;

            }
            get
            {
                return _connectionString;
            }
        }
        public string DatabaseName
        {
            set
            {
                _databaseName = value;
                connection.ChangeDatabase(_databaseName);
            }
            get
            {
                return _databaseName;
            }
        }
        public string ServerName
        {
            set
            {
                _serverName = value;
            }
            get
            {
                return _serverName;
            }
        }
        public string UserName
        {
            set
            {
                _userName = value;
            }
            get
            {
                return _userName;
            }
        }
        public string Password
        {
            set
            {
                _password = value;
            }
            get
            {
                return _password;
            }
        }
        #endregion
        #region Constructor
        public SqlDBAccess()
        {
            _connectionString = ConfigurationSettings.AppSettings["Server"];         //"server=(local);database = db_IFRMS;persist Security Info=False;user=sa;password=@pwd99$02!;connect Timeout=5";
            //DecriptString();
        }
        public SqlDBAccess(string conStr)
        {
            _connectionString = conStr;
            //DecriptString();
        }
        #endregion
        #region Security Methods
        private void DecriptString()
        {
            string[] parts = _connectionString.Split(';');
            string[] words = parts[0].Split('=');
            _serverName = words[1].Trim();
            words = parts[1].Split('=');
            _databaseName = words[1].Trim();
            words = parts[3].Split('=');
            _userName = words[1].Trim();
            words = parts[4].Split('=');
            _password = words[1].Trim();

        }
        #endregion
        #region Connection Method
        public void OpenConnection()
        {
            try
            {
                if (!(connection.State.ToString() == "Open"))
                {
                    connection.ConnectionString = _connectionString;
                    connection.Open();
                }
            }
            catch (SqlException ex)
            {
                Log("Error in open connection", ex);
                throw ex;
            }
            catch (Exception ex)
            {
                Log("Error in open connection", ex);
                throw ex;

            }
        }
        public void CloseConnection()
        {
            try
            {
                if (connection.State.ToString() == "Open")
                    connection.Close();
            }
            catch (SqlException ex)
            {
                Log("Error in close connection", ex);
                throw new ApplicationException("Error in close connection", ex);

            }
            catch (Exception ex)
            {
                Log("Error in close connection", ex);
                throw new ApplicationException("Error in close connection", ex);
            }
        }
        #endregion
        #region ExecuteNonQuery
        public int ExecuteNonQuery(string sqlStmt)
        {
            OpenConnection();
            int rowCount = 0;
            try
            {
                transaction = connection.BeginTransaction();
                command.CommandText = sqlStmt;
                command.Connection = connection;
                command.CommandType = CommandType.Text;
                command.Transaction = transaction;
                rowCount = command.ExecuteNonQuery();
                transaction.Commit();
            }
            catch (SqlException ex)
            {
                if (transaction != null)
                    transaction.Rollback();
                Log("Error in ExecuteQuery", ex);
                throw new ApplicationException(ex.Message);

            }
            catch (Exception ex)
            {
                if (transaction != null)
                    transaction.Rollback();
                Log("Error in ExecuteQuery", ex);
                throw ex;
            }
            finally
            {
                CloseConnection();
            }
            return rowCount;
        }
        public int ExecuteNonQuery(string sqlStmt, bool IsStoredProcedure)
        {
            OpenConnection();
            int rowCount = 0;
            try
            {
                transaction = connection.BeginTransaction();
                command.CommandText = sqlStmt;
                command.Connection = connection;
                if (IsStoredProcedure)
                    command.CommandType = CommandType.StoredProcedure;
                else
                    command.CommandType = CommandType.Text;
                command.Transaction = transaction;
                rowCount = command.ExecuteNonQuery();
                transaction.Commit();
            }
            catch (SqlException ex)
            {
                if (transaction != null)
                    transaction.Rollback();
                throw new ApplicationException(ex.Message);
            }
            finally
            {
                CloseConnection();
                command.Parameters.Clear();
            }
            return rowCount;

        }
        public int ExecuteMulNonQuery(string sqlStmt)
        {
            int rowCount = 0;
            try
            {
                command.CommandText = sqlStmt;
                command.Connection = connection;
                command.CommandType = CommandType.Text;
                rowCount = command.ExecuteNonQuery();
            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);
            }
            return rowCount;

        }
        #endregion
        #region Execute Reader Methods
        public SqlDataReader ExecuteReader(string sqlStmt)
        {
            try
            {
                OpenConnection();
                command.CommandText = sqlStmt;
                command.Connection = connection;
                command.CommandType = CommandType.Text;
                reader = command.ExecuteReader();

            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);
            }
            catch (Exception ex)
            {
                throw new ApplicationException(ex.Message);

            }
            return reader;

        }
        public SqlDataReader ExecuteReader(string sqlStmt, bool IsStoredProcedure)
        {
            OpenConnection();
            try
            {
                command.CommandText = sqlStmt;
                command.Connection = connection;
                if (IsStoredProcedure)
                    command.CommandType = CommandType.StoredProcedure;
                else
                    command.CommandType = CommandType.Text;
                reader = command.ExecuteReader();
            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);
            }
            catch (Exception ex)
            {
                throw new ApplicationException(ex.Message);
            }
            return reader;
        }
        public Object ExecuteScalar(string sqlStmt)
        {
            OpenConnection();
            try
            {
                command.CommandText = sqlStmt;
                command.Connection = connection;
                command.CommandType = CommandType.Text;
                obj = command.ExecuteScalar();

            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);
            }
            finally
            {
                CloseConnection();
            }
            return obj;
        }
        #endregion Reader Methods
        #region Adapter Methods
        public DataTable Adapter(string sqlStmt)
        {
            OpenConnection();
            try
            {
                command.CommandText = sqlStmt;
                command.Connection = connection;
                command.CommandType = CommandType.Text;
                adapter.SelectCommand = command;
                if (dataTable != null)
                    dataTable.Clear();
                adapter.Fill(dataTable);
                commandBld.DataAdapter = adapter;
            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);
            }
            finally
            {
                CloseConnection();
            }
            return dataTable;
        }
        public DataTable Adapter(string sqlStmt, bool IsStoredProcedure)
        {
            OpenConnection();
            try
            {
                command.CommandText = sqlStmt;
                command.Connection = connection;
                if (IsStoredProcedure)
                    command.CommandType = CommandType.StoredProcedure;
                else
                    command.CommandType = CommandType.Text;
                adapter.SelectCommand = command;
                if (dataTable != null)
                    dataTable.Clear();
                adapter.Fill(dataTable);
                commandBld.DataAdapter = adapter;
            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);
            }
            finally
            {
                CloseConnection();
                command.Parameters.Clear();
            }
            return dataTable;
        }
        public void Adapter(string sqlStmt, string tableName, bool IsStoredProcedure)
        {
            OpenConnection();
            try
            {
                command.CommandText = sqlStmt;
                command.Connection = connection;
                if (IsStoredProcedure)
                    command.CommandType = CommandType.StoredProcedure;
                else
                    command.CommandType = CommandType.Text;
                adapter.SelectCommand = command;
                if (dataSet.Tables[tableName] != null)
                    dataSet.Tables[tableName].Clear();
                adapter.Fill(dataSet, tableName);
                commandBld.DataAdapter = adapter;
            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);
            }
            finally
            {
                CloseConnection();
                command.Parameters.Clear();
            }
        }
        public void Adapter(string sqlStmt, string tableName)
        {
            OpenConnection();
            try
            {
                command.CommandText = sqlStmt;
                command.Connection = connection;
                command.CommandType = CommandType.Text;
                adapter.SelectCommand = command;
                if (dataSet.Tables[tableName] != null)
                    dataSet.Tables[tableName].Clear();
                adapter.Fill(dataSet, tableName);
                commandBld.DataAdapter = adapter;
            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);
            }
            finally
            {
                CloseConnection();
            }
        }
        public void Adapter(string sqlStmt, DataTable table)
        {

            try
            {
                OpenConnection();
                command.CommandText = sqlStmt;
                command.Connection = connection;
                command.CommandType = CommandType.Text;
                adapter.SelectCommand = command;
                adapter.Fill(table);
                commandBld.DataAdapter = adapter;

            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);

            }
            catch (Exception ex)
            {
                throw new ApplicationException(ex.Message);

            }
            finally
            {
                CloseConnection();
            }
        }
        public void Adapter(string sqlStmt, DataTable table, bool IsStoredProcedure)
        {
            OpenConnection();
            try
            {
                command.CommandText = sqlStmt;
                command.Connection = connection;
                adapter.SelectCommand = command;
                if (IsStoredProcedure)
                    command.CommandType = CommandType.StoredProcedure;
                else
                    command.CommandType = CommandType.Text;
                adapter.Fill(table);
                commandBld.DataAdapter = adapter;

            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);
            }
            catch (Exception ex)
            {
                throw new ApplicationException(ex.Message);

            }
            finally
            {
                CloseConnection();
                command.Parameters.Clear();
            }
        }
        public void DataSetToDB(DataTable table)
        {
            OpenConnection();
            try
            {
                adapter.Update(table);
                dataSet.AcceptChanges();
            }
            catch (SqlException ex)
            {
                throw new ApplicationException(ex.Message);
            }
            finally
            {
                CloseConnection();
            }
        }
        #endregion Adapter Methods
        #region Error Log Methods
        public static void Log(string Message)
        {
            Log(Message, null);
        }
        public static void Log(string Message, Exception Ex)
        {
            string fileName = Environment.CurrentDirectory + "\\" + "Error.log";
            using (StreamWriter logFile = new StreamWriter(fileName, true))
            {
                logFile.WriteLine("{0}: {1}", DateTime.Now, Message);
                if (Ex != null)
                    logFile.WriteLine(Ex.ToString());
                logFile.Close();
            }
        }
        #endregion Error Log Methods
    }
}

Now I am getting Exception for System.Data.SqlClient.SqlError: "A Network Related Problem" when I am trying to connect with my database.

Please help me to solve this problem.
Thank you.