I'm not sure what's wrong here, since I'm assuming single-player shouldn't be affected by network configuration -- but just in case I tried connecting to multiplayer and was able to connect to a few other players in a game and saw some other players also connecting to me. Tournament runs just fine, but any time I try to run Skirmish, the program sits with the loading icon and the Connecting to Lobby message and never progresses beyond that (and needs to be killed via Task Manager, since there's no way to cancel). Just to see if things were just slow, I started Skirmish mode and left Demigod on the loading screen. It was still there over twelve hours later.
I tried searching the forums but didn't see anyone else with this particular problem. What surprises me is that my network appears to be Demigod-friendly, and Tournament runs fine, so why should Skirmish mode be a problem?