Help Can I get an RMA for my CPU?

My desktop cut out 2 weeks ago (it wasn't a power cut, just my desktop cut out) and since then it wont power up. I've been trying a few things to see what the problem is.

Things I've done:
- Jump start the PSU by itself (it worked fine)
- Jump start the PSU whilst running a fan (it worked fine)
- Jump start the PSU whilst connecting the two 4 pin wires into the motherboard (this causes the PSU to not power on)
- Connect just the 20+4pin into the motherboard (the motherboards green LED stays on, but when I try to power on the desktop the fans run for half a second before powering down again)
- Connecting 20+4pin whilst teh GPU isn't connected (powers on for half a second before switching off again)
- Connecting 24 pin from a DIFFERENT PSU (300W) whilst GPU isn't connected this doesn't even power the desktop on (not surprising but worth a shot)
- Tried the 650W PSU in a different desktop and it works fine

Things I believe can't be causing the problem:
- Power Supply (It works on a different desktop)
- Mother Board (I had it RMA'ed and they said it works fine)
- Bad Memory (They tested this during the motherboard RMA)
- Graphics Card (I removed the graphics card from the motherboard, but it still doesn't power up)

That leaves just the CPU, right? I bought the CPU from SCAN 6 months ago - Invoice No: 00E1851950

Can we conclude that the CPU is the cause of this problem and that I should get it RMA'ed?

Thanks!

My computer hardware on the affected desktop:
Motherboard: Asus P8Z77 V LE
CPU: Intel Core i7-3930K
PSU: OCZ ZS Series 650W
GPU: Radeon HD 7950
RAM: Corsair Vengeance 4GB x2
HDD: Seagate Barracuda 1TB
SSD: Intel Cherryville