Graphics card Freezes, resets, and repeats.?

When I play certain games (Mass Effect 2 [ ME1 runs fine], Batman AA, The Godfather II) the game will run fine at high settings, then about a few hours in it will freeze, my monitor will go black, say "Monitor Going to Sleep", then the game will be back but with weird blue pixels randomly popping up. ... show more When I play certain games (Mass Effect 2 [ ME1 runs fine], Batman AA, The Godfather II) the game will run fine at high settings, then about a few hours in it will freeze, my monitor will go black, say "Monitor Going to Sleep", then the game will be back but with weird blue pixels randomly popping up. Under the game a message pops up saying that your Graphics card has "frozen and reset itself". I have tried just playing with the blue squares, but it will freeze two more times (second one within around 5-8 minutestes. Final one only a minute or two after that.) then it will no longer run my game. If I close the game before the third freeze, I can run the game but the blue squares still show up. And the freezing happens faster. Also, when the third freeze happens and closes, I can still use my basic computer functions, but when I move a window around it doesn't show it move. It only shows where it is and where it stopped. I am using an "XFX Ati Radeon HD 4650 1GB GDDR2 Memory" (It has a gargoyle on the box.) Since the initial purchase (when it was already doing this) I have upgraded basically every part of the computer.
Here are the Specs:
Graphics -- XFX Ati Radeon HD 4650 1GB GDDR2 Memory
RAM -- 2 1GB Sticks. DDR3.
Hard Drive -- 1 TB + 1/2 TB (Don't remember the GB's, sorry)
Power -- Corsair 650W
Motherboard -- ASUS M4A79XTD EVO.
Processor -- New, Fits the motherboard, pretty good, but not EXTREME! (Can't find the box...)
Case -- SopranoRS Thermaltake from Best Buy. Supposed to give better cooling.
Fans -- Plenty of them. Though not all near the graphics card.
Sound -- not new, came with old computer, I don't think this is the problem...
OS -- Windows XP Media Center Edition, SP 3.

Please do not give me crap about still using XP. I really don't want to go through the installation of Vista, and 7 so please only mention upgrading it if you think it is actually the problem.
Many other games work for hours on end and never freeze (GTA IV, ME 1, Borderlands.) I have the newest drivers, I've checked to see if it's installed properly, and made sure it gets good ventilation. I have NO idea why it does this, especially if it's just for certain games! It has a Life Warranty, and it was the first thing I ever added to my PC. But again, because it works for some I don't think it's a bad card.

If you can help me in any way (If you want to buy the Vista and 7 installs for me, and send them to me...) I would really appreciate it. If you don't know, please don't say "Dude that sucks! Never heard of anything like that." I don't want pity, I want a working PC. If you can help then I would Really appreciate it. If you can't, that's okay, just please don't spam me.
Update: Thank you all for your answers, and so quickly too. To Harley: I agree with Fordry saying it probably isn't the memory, but I won't shoot down anything yet. If you can provide proof of it actually effecting negatively, I would thank you greatly. To Fordry: The only thing with your answer is that your link... show more Thank you all for your answers, and so quickly too.
To Harley: I agree with Fordry saying it probably isn't the memory, but I won't shoot down anything yet. If you can provide proof of it actually effecting negatively, I would thank you greatly.
To Fordry: The only thing with your answer is that your link doesn't have the actual download. Is there another site that I can get that program? I don't want to start the process without being able to finish. I think you can understand why...
To Raff: This is one I've tried, but not fully. I played Batman in compatibility mode, but it still had the early symptoms just before a freeze/restart cycle(game slows down Drastically). At that point I shut down the game, so I am unsure whether or not your method works. I will be trying it and if it does work I will be forever in your debt.

Again, thank you guys for your assistance. Just having these answers has given me some hope that my computer can work well!
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