Sounds like a DNS issue. Ping the server by name and then by IP address. If IP address works but the name does not, the issue will definitely be your DNS entries.
This, of course, is assuming you have the permissions for the share set correctly and that file and print sharing is enabled, which it sounds like is the case.
ipconfig /all will let you see from the client side which server the DNS service is coming from. After tweaking your DNS server, run ipconfig /flushdns and then ipconfig /registerdns on the client and then do the ping test again. If the DNS is properly set you should get a proper resolution for both test pings and then be able to map by name via the GUI.