I got this error immediately after installing VS2005 & SQL Server 2005 Express and trying to establish my first connection using the new server - not a good start at all - and by the looks of it, it's happened to many hundreds, if not thousands, of others too.
Generally this error occurs if you cannot connect to the SQL server - as the message says (no sh*t). However, what's not obvious is why...
First suggestion is to make sure that you specifiy the instance name as well as the server name (christ knows why, but when MS refer to "Server Name" they really mean "Server Instance Name") eg if your server was named 'bigturnip' then you need to specify 'bigturnip\sqlexpress' (where sqlexpress is the instance name - this one just happens to be the default used by SQL Server 2005 SQLExpress).
If that doesn't help, then go into the SQL Server Configuration Manager and make sure you've enabled Named Pipes & TCP (if you're using it) and also go into the Surface Area Configuration tool and make sure you've set it for local &/or remote connection for the connection types you want to use. Then restart the SQL Server (instance) service.