Computer hanging when playing games

[ultimatum]

Ok, i had this crappy ^#%*&@# problem for sometime, thought i had fixed it, but no...

My computer is a 2Ghz, 512DDR Ram, GF3 Ti 200 64 DDR RAM graphic card, running on WIN XP platform.
My computer can run perfectly well, day and night turn on whilst connected to the internet, basically it can run forever when not running heavy applications like games.

Previously my computer hangs when im playing a game after some time, and the game would be a 3D game, not 2D.
Meaning i can run games like Starcraft, Diablo, but i can only play games like GTA3, Elder Scrolls Morrowind, Dungeon Seige etc for only like 10-15mins, 30mins top before the computer will hang.

I trouble shoot my computer, and found that my ADSL modem, which used a USB port and needs no power supply hence using power from the CPU itself. I believe that this eats up the power that is needed to supply my graphics card. My theory is due to insufficient power to the card the computer hangs itself. Secondly, when i turn on the air-con in my room or weirdly play the computer at night, the game will also run longer, having less hangs, especially when playing Morrowind which is a detailed rich graphics game.

True enough, once i pulled the plug which connects the modem to the CPU, my 3D games can run pretty well, for some time. Though it will still hang after some time, but upon restarting it works well.
I was satisfied and didn't bother with the occasional hangs.

Now, when im running CnC Generals im having the same problems again and i have disconnected the modem.I even turn on the aircon, but my problem is still there. The game always hangs after about 20 mins of gameplay.

I wish to end this problem once and for all....
what the crap is wrong with my computer?
For one thing i need more fans, but can it be the graphic card's fault? or the motherboard?

Can you recommend any diganostics program to me? Thank you very much. Any help or suggestions or better, solutions given will be greatly appreciated.

[Baser-X]

If you're running really hot, this could be the source of your problem. I don't have time to track down links right now, but there are programs that will monitor the temp of your board/processor/video etc... some of them will also check your fans to make sure they are working correctly.

[shingalated]

if you need to unplug your modem to get enough power, you may need a bigger power supply, also you may be able to connect the modem with a network cable. i know mine has a usb port and an ethernet