I was experiencing the lock-up's everytime I clicked the mouse or pressed a key during the intro movie.
After reading the boards, my solution was to (Note that I am using an XP system so you vista folk will have to adjust paths):
1. Rename the movie file (dg_intro.bik) found in C:\Program Files\Stardock Games\Demigod\movies
2. Start Demigod, DO NOT use the mouse or keyboard...watch the short AD movies, and get to a black screen.
3. Wait patiently (1 minute maybe a bit more) and the menu will display.
For me the key was step 3, as there is no indication that the system is doing anything...I was thinking it was crashed. I running a Core2 Duo at 3.3 Gig and am not very patient.