I cannot explain the original posters' problem, as it works in one system, but not another. This makes no sense...
... however I can comment on Spazzy Chicken's problem, as the same thing happened to me.
It is my personal belief that there has been a bad batch of 6600GT chips released by NVidia to its board partners. I have seen this as a widespread problem from an assortment of board venders, but always relating to the 6600GT (I think the AGP version in-particular), and always revolving around the "play a game or benchmark for one minute then freeze" problem.
As I mentioned, I had this EXACT SAME PROBLEM occur with my card (a BFG 6600GT OC), that I had mail-ordered... I got it in, ran all 2D just fine, but after running any benchmark or 3D application/game, the card would ALWAYS FREEZE after about 1 or 2 minutes of running.
I tried every driver update, every BIOS tweak, even putting the card in three differant systems... nothing I could do would change/solve the problem and it had the same problem in every system.
I scanned the net and found TONS of other people with similar problems and it seemed to be the 6600GT that was the culprit (various brand names). Anyways, long-story short, a few folks recomended stop toying with the card and stop trying to fix it, just realize you got "one of the bad chips" and return it for a replacement 6600GT... this I did... I got a new BFG 6600GT from the same store and low and behold, without a single tweak, it worked like a charm in my system running all games and benchmarks without a sweat.
LESSON?
A good percentage of 6600GT chips are faulty and will immediately fail on any benchmark or 3D game... if you get one of these, just forget trying to fix the problem, the chipset is bad and you should return and get a replacement... as I stated, the 2nd BFG 6600GT I got was fine and dandy! I am VERY HAPPY with my 2nd card!