The connection string looks to be wrong -
Here are some examples which might help you,
For your case, it should be -
SqlCeConnection conexion = new SqlCeConnection("SERVER=188.8.131.52;User Id=dbowner;Password=corpdgo;DATABASE=GPODGOATQ");
System.Data.SqlClient.SqlConnection conexon = new System.Data.SqlClient.SqlConnection("Server=184.108.40.206;UID=dbowner;PWD=corpdgo;DATABASE=GPODGOATQ;");
Now to connect from mobile(Windows), you cannot use ADO.NET as it is unavailable in silverlight.
To connect to sql server CE, you can google (how to connect swql server CE from windows mobile)
If you want to connect to external sql server hosted in database server, try to use WCF or web service to write public exposed methods that you can consume from windows mobile.
Hope this helps.