I was having the exact same issue. On a hunch, I did the port forwarding thing in this guide: http://themonk.ca/Monk/Networking_and_DEMIGOD.pdf I haven't had any issues since then. Also, I think it's important that you disable UPnP like it says in the guide. I'm guessing that it's wanting to connect to some online server during each map load - even for single-player games. Hope that helps, it seems to have worked for me so far.
NecoMachina
Ya, I'm having a similar issue. Game loads fine, not having any issues at all getting to the main menu. When I go to Single Player => Tournament => Continue => Fight! => Continue, the game seems to lock up more than half the time while it's loading the map. Sometimes it happens on the splash screen that says Demigod at the bottom and a little animated progress bar; the progress bar stops moving and it just sits there until I kill the game in the task manager. Sometimes it happens