UPDATE:
Our home connection seems to start coughing every now and then. Earlier today, I couldn't even get a browser anywhere before restarting my computer twice and the modem once.
The networks seemed to work nicely now, but then I hit error with Dominions. It just throws a "Network Error" at me when I try to start it as a server.
EDITED
Okay, DomII didn't work because the port 1111 was already in use... by the game itself! I used --textonly switch to have the game to run insivibly, but didn't think it worked because I didn't see anything.
So, it seems there are no problems with Dominions on this end.