How to backup SQL Server database once evaluation period has expired
I found a solution myself. Once SQL Server Management Studio expires the evaluation period it will not open anything. It shows go to this site to upgrade product or something else.

First, change the system date to 2 or 3 days back, then open the SQL Server Management Studio. Now you might get this error:


  A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections.
  (provider: Named Pipes Provider, error: 40 - Could not open a connection to SQL Server) (Microsoft SQL Server, Error: 2)


Now follow this step:

Check if your SQL Server service is up and running properly:


Go to All Programs > Microsoft SQL Server 2008 > Configuration Tools >
SQL Server Configuration Manager > SQL Server Services
Check to make sure SQL Server service status is Running.


In addition, ensure that your remote server is in the same network. Run sqlcmd -L to ascertain if your server is included in your network list.