After about 10 minutes of running, my computer will hang, exhibiting the following symptoms:

1. Both monitors act as if there is no image being sent to them (on, but blacked out)
2. The CAPS Lock key on the keyboard will not respond.
3. The computer appears to still be running: CPU Fan is whirring.

When I reboot, Windows says "The previous shutdown was unexpected."

I've enabled the 'don't automatically restart' on an error, and asked the computer to make a memory dump whenever it crashes, but it hasn't done either.

The problem is that there's no bugcheck for me to go off of, so there's no way for me to determine what the cause is (I think).

Here are my system specs:

• Intel Core 2 Duo E6750
• Gigabyte P35C-DS3R w/ 4.00 GB (DDR2 Ram)
• Nvidia 8800 GT
• Windows 7

I've tried running the Windows Memory checker, but the system also freezes when using that after about 10 minutes as well.

How can I diagnose the problem with no bugcheck and no ability to run a memory checker?

Update

Running Memtest86 also causes the computer to crash (looks like it doesn't make it through a full pass - it was only running for about 10 minutes when the PC stopped responding).