PC Shuts Down in Game Play

I just Built a new PC with the following:

MB- MSI K9VGM-V
Processor- AMD Athlon 64 3500+
Power Supply- Hercules ATX 500 watt
HDD- Maxtor 160GB (2 hdd's in system, both are the same)
DVD/CD Drives- LiteOn DVD/CDRW & WriteMaster DVD-RW/CDRW
Video- GeForce4 MX440 128MB PCI
Memory- Kingston 1024GB
Fans- 1 on power supply, 1 in the door, 1 at front of system,
and CPU fan
Problem: Computer shuts down after 5 - 10 minutes of game play. The power light blinks and I have to hold in the power button to finish shutting the system down and then turn the system back on.
This problem has been going on since I built the system.
The only games I can play are the ones that comes with Windows XP(FREE CELL, HEARTS, SOLITAIRE, SPIDER SOLITAIRE, ETC...) and internet games like on Yahoo.com or POGO Games.
I started playing games with the on board display adapter and it would shut down after 5 - 10 minutes of game play. So I installed a video card, same thing happens.
I checked for "Wake On LAN" in BIOS, it is disabled.
I have checked the system tempurature and it never gets over 103 degrees.
The computer is extremely clean, I just built it a month ago and I clean it twice a week.
Games that I play are Game Of Life, Treasure Seek Games, Roll Playing, Board & Card Games.
I hope someone has some idea of what is going on here and how to fix it.
It is not fun, not being able to play any of my games.
 
There are a few dif things that can cause this to happen.

since really the games you are talking about are just normal applications than I doubt the vid card. So lets move to the memory. Test the memory using memtest86 which can be found for free. run at least 4-5 cycles and look for errors. I would also have the power supply tested properly at a pc tech store.
 
I have already tested the memory, I just forgot to put that in my original post. No errors on the memory. As I mentioned before I just built this PC a month ago. Everything in it is brand new. However, I'm not ruling out the PSU as I know things can be bad from the start. But let hypothetically say the PSU is not the problem, what other solution could there be?
I will test the PSU, just to rule it out.
 
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