First place I would check is the SQL Server error log. You can get this through the file system, and it is a text file, so you can open it in notepad. Check to see if you are getting login failures. If you are, you should get much better information here that normally is not reported to a client that has failed to log in.
If there are no failed logins in evidence in the errorlog, you very likely are having problems getting to the instance in the first place. Things to start checking here would be local firewall settings, or if the IP address resolves from the client attempting to connect.