Area-51 ALX Desktop shuts down randomly when idle

I’ve been on holiday for a month, and when I got back I found my computer now shuts down randomly, with no warning, nothing in the Event Viewer, and no blue screen.

Sometimes it will shut down in 5 minutes to over an hour during either idling or actual use. However, it usually happens when I’m playing a video (though that might be a coincidence, since it will also shut down when I'm not using it).

Things I’ve tried so far:

- Dell Hardware Diagnostics (no problems)

- Heavy 3D Benchmarking Tests (does not shut down)

- 2 Hour CPU Stress Test with Prime95 (does not shut down)

- Virus scans (no malware)

- Dust cleaning (might still be some left somewhere)

I’m not sure what other kinds of things I must check for to find out the problem. 

I'm just trying to make sure it's not something other than the PSU - before I fork out the money for a replacement.

Thanks in advance!

Computer specs:

Alienware Area-51 ALX

OS - Windows 7 Ultimate 64bit (English)

Motherboard - Alienware 0XDJ4C

CPU - Intel(R) Core(TM) i7 980X (3.33GHz, 12MB)

Power Supply - Anodized Satin Black Chassis 1.2KW Power Supply

RAM - 12GB (3X4GB) DDR3 SDRAM 1333MHz Memory

Graphics - Dual NVIDIA(R) GeForce(R) GTX480 1.5GB DDR5 - SLI

Hard Drives (4x) - 1TB-7,200RPM Hard Drive, 1TB-7,200RPM Hard Drive, Samsung HD103SJ 1TB 7200 RPM Hard Drive, Samsung HD103SJ 1TB 7200 RPM Hard Drive