See if the local Network Diagnostics report that the Mac is connected to the Internet, or if there's an issue. > System Preferences > Network > select the network connection > Assist me... > select Diagnostics.
Also check the local server setup for various DNS services and network errors, by logging into the server and launching Terminal.app from Applications > Utilities and entering the following harmless, diagnostic command:
sudo changeip -checkhostname
That requires your administrative password. That'll generate a one-time sudo-related message, if it's the first time you've used sudo. You'll then see some local host network information, then an indication that no changes are needed, or possibly some diagnostics.
And to confirm: you're running OS X Server 10.6.8?