A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible.

check these things
1. Make sure your database engine is configured to accept remote connections(I you are using centralized database)
•Start > All Programs > SQL Server 2005 > Configuration Tools > SQL Server Surface Area Configuration
•Click on Surface Area Configuration for Services and Connections
•Select the instance that is having a problem > Database Engine > Remote Connections
•Enable local and remote connections
•Restart instance

2. Check the SQL Server service account
•If you are not using a domain account as a service account (for example if you are using NETWORK SERVICE), you may want to switch this first before proceeding

3.If you are using a named SQL Server instance, make sure you are using that instance name in your connection strings in your ASweb P.NET application
•Usually the format needed to specify the database server is machinename\instancename
•Check your connection string as well

Please go Control Panel\All Control Panel Items\Administrative Tools\services and start SQL SERVER(SQLEXPRESS).it will work.

You can check if your computer name and the user name is same or different. if same please change the user name or computer name. u can give it a try, coz i tried all blogs, forums, Google search and lots of things for almost 1 year to solve this problem. finally i did this and it solved my problem.

Try adding a , and a port number as in ",1433" to the end of your connection string.

Its possible that WMI or some other service dependency required to resolve the database instance name wasnt working on you local machine.

Manually specifying the port will resolve this.

Try these Commands =>

C:>sqllocaldb stop MSSQLLocalDB
LocalDB instance "MSSQLLocalDB" stopped.

C:>sqllocaldb delete MSSQLLocalDB
LocalDB instance "MSSQLLocalDB" deleted.

C:>sqllocaldb create MSSQLLocalDB
LocalDB instance "MSSQLLocalDB" created with version 13.0.1601.5.

C:>sqllocaldb start MSSQLLocalDB
LocalDB instance "MSSQLLocalDB" started.

Above all are meaning full solutions but resolved this by Restarting the machine.Try this if not work any of the above solutions.

If you are using mac then this issue occurs due to a mistake in Connection String. Since docker is required so the connection is made by considering the server on the remote machine. Thus in Connection String, the Server is provided and it should be the IpAddress of the mac machine followed by the port number of the server.

"Server=MacMachineIpAddress,portnumberOfServer;Database=db_name;User Id=sa; Password=**yourPassword**;"

Hope this helps.