What OS are you running?
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Biggest Troll on the forums? I'll give you a hint:
@Kheldarn - Win7 Ultimate x64.
Okay, I (with help from my bro) troubleshooted the problem and so far we've ruled out problems with the processor, albeit the heat sync was disconnected and the connection's health is degenerating slowly, thus CPU temp went up a little. Testing memory (one stick at a time, 2GB right now, 6GB total.) right now, have yet to encounter problems~
A problem did occur. I tested the computer by running L4D2 and leaving it sit, and it crashed soon after. I think we're going to nuke the problem by formatting the system drive, but so far we're just leaving it alone for now.
My first thought is to make sure your dirvers are all up to date...
I strongly suggest heading over to the Technical Issues & Bugs section of the forums and starting a thread there describing what's happening, and what you've already done.
Then, post a CoH Helper and a HiJack This log. The folks in that forum are some awesome tech wizard gurus, and they might just be able to deduce the problem and give you the solution.
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Biggest Troll on the forums? I'll give you a hint:
Graphics card seems to be the problem. Ran TF2 for the same amount of time as L4D2 (using a different card of course) and there were no problems.
What confuses me is how a malfunctioning graphics card is able to
1. Crash and reboot the computer.
2. Hard hang the computer, requiring a hard shutdown.
3. Prevent the computer from getting past the bios.
All of these problems were fixed by switching to a different graphics card.
.. 
Computers are magical beasts, and nobody can predict what little thing will make it asplode...
Glad to hear you got the problem fixed, however!!
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Biggest Troll on the forums? I'll give you a hint:
indeed GPU Cards are strange beasts, I had an old 6800 Ultra that when it started to crash would first just produce artifacts, then in progressed to halfscreening the computer, then it started hanging the computer, and finally would go to a black screen with everything still running...if I uphooked and connected to onboard graphics, everything was fine. This all happened within 2 days! O.o
Computers are so much fun!!! 
Global:
@Necromanis
If fun means extremely expensive *cough* $1600 build *cough*
then yes, they are VERY VERY fun.
Sorry for another double post, but my computer is having unexpected 'technical difficulties', to where not even an hour of simply idling, it crashes and reboots.
As soon as I get this cleared up, I'll probably set up a new (and longer) subscription to CoX with my b-day monies.
(Yay safe mode for being so reliable...)
Sub ends on July 26th D: