Computer shutting down randomly

Hi everybody, I'm gonna make this as easy to follow but if you see any spelling mistakes it's because I'm trying to type this from my iPod touch

Problem

Corsair 650TX 650W power supply randomly shuts down in the middle of watching a vide in hulu after ten minutes or I'm playing a game

Details

Computer was bought on January 29 based on what I've seen when searching this topic is that it either is the power supply, motherboard, graphics card, ram, or OS. Here is a list

Sapphire Radeon HD 4850 1 GB
Corsair 650-TX 650 W ATX12V/EPS12V SLI Ready CrossFire REady 80 Plus Certified and so on..
OCZ Platinum 4GB 2(x2GB 240 Pin DDR2
Microsoft Windows Vista Ultimate SP1
Gigabyite GA-EP45-UD3P

Sadly no I don't have another system to test my components on and a spare psu to work on. I've tested it out on while the case lid was open yet it still shut off while playing assasins creed on medium settings even though I have a pretty high end graphics card. However it doesn't shut down when playing other games like spore on high setting that run at least 20 FPS with other programs (Firefox, Skype, etc...) in the background. It also shuts down when trying to start up again after a random shutdown.
So you may be right about the heat issue

So in short:
It turns off only when playing Assasins creed and watching videos on hulu longer than 10 minutes

plus

when turning it back on after a random shutdown there is a 70% chance that it could shut down again.