Beagle
I REALLY hate to disagree with Jim, but I have seen this happen on two different systems. both times the system would shut down without warning, just "go blank" after reaching a certain temperature and that didn't take long.
In both cases, the system would do exactly as you described. the screen would go blank, the fans would all still be running, no beeps or anything from the computer.
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both computers I removed the cpu fan, cleaned the thermal grease off of the cpu, replaced the fan with a new one using new thermal grease and everything worked like a charm.
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I have a similar problem on one machine, but mostly is that one can not reboot/restart the machine as it might not come back up. All I gotta do is wait 5 minutes, reset the power supply and it comes up fine.
The motherboard has no new drivers since the original, thus the BIOS can not be updated, and yeah ... that computer is about 5 to 6 years old, and it is pushing a GTX 760 ... and it's actually faster on WoW switching zones, than my SS machine with twice the memory and a faster video card (GTX 970).
This 2nd computer is only keeping back up copies and hard drive is not an issue. The same thing was happening before with W8 and W8.1 ... and I'll just take it a bit further and upgrade the motherboard in the next year or so.
My guess, and it is a GUESS, this is an issue with the motherboard, and it could be related to heat, however, it would be odd that it would heat up after so many hours, when most computers are designed to be able to stay on without overheating. I'm guessing that it won't get better either, and it might be time to swap out to a new motherboard?