Error message: (provider: Shared Memory Provider, error: 0 - No process is on the other end of the pipe.)

Typically, to troubleshoot this, you go to SQL Server Configuration Manager (SSCM) and:

1. ensure Shared Memory protocol is enabled
2. ensure Named Pipes protocol is enabled
3. ensure TCP/IP is enabled, and is ahead of the Named Pipes in the settings

Maybe it can help: Could not open a connection to SQL Server

I had this same error message, turns out it was because I didn't have mixed mode auth enabled. I was on Windows Auth only. This is common in default MSSQL deployments for vSphere, and becomes an issue when upgrading to vSphere 5.1.

To change to mixed mode auth you can follow the instructions at http://support.webecs.com/kb/a374/how-do-i-configure-sql-server-express-to-enable-mixed-mode-authentication.aspx.

I had the same error by in SQL Server Management Studio.

I found that to look at the more specific error, look at the log file created by the SQL Server. When I opened the log file, I found this error

Could not connect because the maximum number of ’2′ user connections has already been reached. The system administrator can use sp_configure to increase the maximum value. The connection has been closed

I spend quite some time figuring this out. Finally running the following code fixed my problem.

sp_configure 'show advanced options', 1;
go

reconfigure
go

sp_configure 'user connections', 0
go

reconfigure
go

More on here and here

Edit

To view logs search for "logs" on windows startup button, click "view events logs". From there go to Applications under "Windows Logs". You can also choose "System" logs to see system wise errors. You can use filter on current logs by clicking "Filter Current Logs" on right side and then select "Error checkbox".