I've got (what I believe to be) a fresh installation of Server 2003 R2 (SP1), and while I've got perfect LAN connectivity, I can't access the Internet. I've tried pinging websites through Command Prompt, and I still get nothing. I've never used Server 2003 before, so I've got no idea what to look for. This box is plugged into the same switch as the computer that I'm typing this up on, so I know it's not that.
I checked, and I don't think that this is a dupe of this question, as I am about 99% sure that someone installed Server 2003 on this box then never used it - I doubt that it ever had internet connectivity to begin with.
EDIT: Apparently, I've got basic network connectivity now... I can ping the router at 192.168.0.1, but I still can't connect to the internet.
You've got layer 2 and layer 3 connectivity on the local network, what you may not have is layer 3 connectivity beyond the local network or you may have a name resolution problem. Try to ping and tracert to 8.8.8.8. If that's successful then your problem is a name resolution (DNS) problem and you'll need to look at the DNS settings on the server. If you can't ping or tracert to 8.8.8.8 then you've got a problem at the router, which could be a NAT problem or a firewall rule problem..