Try using fully qualified server name... error message shows "error connecting to server\instance".

Change connection to look for servername.domain.com\instance

(of course by domain.com, I mean whatever the fully qualified name of the server is)

Also- get down to basics. Set aside managment studio for now and go to the command line. Can you ping the server? can you ping it using fully qualified name? can you telnet to it over port 1433? It's a named instance, what port is it listening on if not default?