Mystery problem: Video cuts out randomly all the time

[CGTMachine]

This computer was build in July 2011 and the problem began in November. I updated the BIOS, which seemed to resolve the issue until it reappeared yesterday. The computer runs perfectly fine until anywhere from 5 minutes to several hours after boot the video will cut out as if the monitor was unplugged and it does not return. The audio and wireless connection occasionally go out, though when I had a disc burning and the video went out, the disk burned just fine. Afterward, when I restart the system (it responds to the power button and I can hear the log out and shut down chimes), the system will reboot without any video, though it will POST fine and I can hear the startup chime as well as use my USB keyboard to type and enter my password to log in, just no video. This repeats anywhere from 2-15 times until eventually the computer boots fine, and then 5 minutes to several hours later the problem reappears. As far as I can tell, all of this is random. It also happens in both XP and Win7, during full boot up, safe mode and even at the BIOS configuration screen.

Steps I have taken:

Re-seat the RAM, GPU and CPU twice; check all power connectors; check all voltages; update BIOS to latest stable and beta versions; update all drivers; fresh installs of XP and Win7; run CPU and GPU stress tests; tried new monitors and HDMI cables. None of this returned any results, there are no crash dumps or other events being logged in Windows, no soft/hardware changes have been made that could have brought this on. Curiously, the computer has a telling sign for when it will boot with video: whenever I turn it on and the CPU fan immediately kicks into its highest RPM for a few seconds before slowing to normal, it always boots fine with video; if I turn it on and the CPU fan doesn't start going as fast as it can for like 3 seconds, I know the video will not show up.

At this point I'm assuming it's hardware but I have no idea what so any help would be appreciated.

Specs
MoBo: Asus Crosshair IV Formula
CPU: AMD Phenom II X6
GPU: Sapphire Radeon 6950 2GB
RAM: 8GB Ripjaws
PSU: Antec EarthWatts 750w

 

[Raiddinn]

What sort of hardware do you have on hand to test with, or accessible from a friend or family member?

Can you try plugging the computer into a TV instead of the monitor?

 

[CGTMachine]

What sort of hardware do you have on hand to test with, or accessible from a friend or family member?

Can you try plugging the computer into a TV instead of the monitor?

What do you mean by hardware to test with? I don't have any other desktop components around like other RAM or MoBos. However, I did try it with a TV and it had the same result.

 

[Raiddinn]

What I mean is that it is easiest to troubleshoot failed hardware by replacing hardware of questionable status with known working hardware.

Something like a failed motherboard can be really hard to diagnose without having another similar motherboard you can put your components in to see if it performs any differently.

RAM isn't hard to test with MemTest86+, but most other hardware is quite difficult to test if you don't know whether it is good or not.

You can take your video card and put it in someone else's computer and see if it works, for instance, but only if you have access to another computer to put it in.

That is why I want to know if you have any friends or family or whatever with accessible computers.

It looks fairly likely the failure is with a hardware component and I need to know the resources at my disposal to help narrow down exactly which hardware device is causing the problem.