Doh! I have a fair bit of Linux experience, but that actually hindered me... (Why on Earth does the command prompt redirect output to files only, instead of displaying it in the console too?)
Anyway
If you want to run the game in its 'try to tell us what's wrong' mode, you should go to Start -> Run -> Enter the path to your dominions executable in quotes, add -ddddd at the end, and attach the resulting log and sterr/stout files for public viewing. So something like: "C:\Program Files\dominions3\dom3" -ddddd (with the quotes as they appear)
I cannot promise you'll find any particularly illuminating information that way, though... still, I think it's worth a try, especially if it's just a software issue somewhere.