Here I go...I just built this system that includes the following:
Gigabyte GA-P35-DS3R Motherboard,
Intel Core 2 Duo E8400 Wolfdale 3.0GHz,
ATI Radeon X1900gt Video,
Mushkin 4GB(2 x 2GB) 240-Pin DDR2,
Seagate 320GB HDD.

I used the X1900GT and the HDD in a previous build with no problems. Now with this new system, everything seems ok, computer runs very fast and seems stable. Until I try to play a game, I can get about 20 seconds into the game and suddenly my system reboots. Just like that! The computer shuts down and restarts. I installed Mark 3D and started the testing and just 20 seconds into the first test, my system restarted. I tried this several times with the same results. I'm stumped! I have installed the latest bios and all drivers are updated to the latest versions. I did the Mem Test and ran it for 30 minutes without a hitch.

sounds like a heat problem... get Prime95 and Speedfan ... prime will stress cpu while speedfan measures temp. once the temp of the CPU goes to a certain point the machine will reboot to protect damage.

You also didnt list your PSU which could also be the issue. Not enough power = no machine

Chookman, My Power Supply should be enough, though, I am no pro. Any it's a "Coolermaster Extreme Power 600W". Model RS-500-PCAR. It's rated at 500 Watts continuous. I downloaded the 2 programs you suggested. I am not smart enough to figure how to use the "Prime 95". I ran the speed fan though and could see I had one (Fan 2) that had no rpm and that was the one getting hot. How do you tell which is which? I actually put a thermometer on the chipset Heat Sink and in a short time it got very hot, the others stayed much cooler. I wonder if they make a fan to fit that big Heat Sink? I think that's my problem. Thanks for your suggestions...