I've had this problem with another game. Turns out the disk had a bad scratch, but not bad enough my Game Dr. couldn't fix after several run throughs.
I believe your problem is with the disk its self having some sort of damage or is unclean given it happens during install, but I wouldn't rule out the drive it's in either. I suggest cleaning the disk and the drive and see if that works.
Also, heres the tech support forum for Demigod: http://forums.demigodthegame.com/forum/526