I have SQL Server 2005, 2008 and 2012 installed on my Windows 7 64bit PC.
Data Source=adamssqlserver
is wrong, should be:
Data Source=lpc193\adamssqlserver
This can be seen in the Server Explorer screenshot you attached. Your connection string is looking for a computer calls "adamssqlserver", whereas your database is a named instance on your computer, which is called "lpc193", so is addressed as lpc193\adamssqlserver