This may be way out in left field but maybe enabling ping for the sake of your investigation may help establish the fact that you can actually see the machine.

Now if the sql client network util only has TCPIP and the server only has named pipes then I fail to see how that is going to work. You can add TCPIP to the server.

Further I believe that named pipes requires that your connection request must first log onto the server before it can log onto SQL server. Thus if you are using named pipes then you may want to confirm that you can connect to a share that is set up on the SQL server (if you can connect to a share then you should be able to connect to the SQL server).

TCPIP does not require that you must first must first log onto the server so it would seem that adding TCPIP to the server is a cleaner way to test your issue rather than changing the client to named pipes. Well, thats the theory anyway.

Also make sure that when using TCPIP that the both client and server are set to same port number (change the client port to the server port).

Further, you should also look at the current SQL Server log and determine what SQL Server is actually listening on. It will tell you what netlibs are being used and what port is open. Be aware that the server network util settings can be changed but the settings dont come into effect until after a restart of the SQL service - thus you need to know the current settings thus the reference to the SQL log. Be on the lookout for reported errors such as failed to bind to port.