I don't think the disks are scratched - there are no visible scratches anyway. The game installs and runs fine on my brother's system (Athlon 64 with GeForce 7600 GT running Win XP) and installs under Wine on my laptop (Pentium M, GeForce Go 6600 GT running Ubuntu), though I can't play there until I work out some of the kinks in Wine, which is a topic for another forum.
I don't think it is a driver problem specifically, as my bro's system uses the current nvidia drivers as well. I suspect that nvidia made some change over the past year and a half or so to their drivers that breaks whatever KOTOR uses to detect the 8800's specs, but given that the problem persists even when using older drivers I don't think that is the source of the problem. Other games work fine for me, so it doesn't appear that my card is fried either.