A few days ago, after being on computer for about half an hour it randomly shut off by itself. I opened the case and cleaned all the dust out, turned it back on accordingly, and after being on another 30 minutes or so it shut down again. Sometimes I noticed the fan on the processor stopped spinning so I figured that was the problem, I made sure no wires were touching the fan. But it kept shutting down and at quicker intervals each time, to the point that it would instantly shut off after being turned on. Then sometimes it would come on and stay on but there instead would be no image on screen.

Anyways long story short, I took to the shop, and the guy said that when he took out my video card and put his in that it had been running an hour flawlessly. So he assumed its my graphics card.

One person told me that it sounds like overheating(my assumption) and that the computer guy probably put in a lowered power video card which resulted in it staying on without shutting off.

I wanted a second opinion and took the computer to Best Buy and they said that they tried a different power supply and a different video card and the computer would not boot and came to tell me that it was my motherboard. So now I have two different responses from two different places. And so it does seem to be my motherboard, but before I go out and purchase a new one, I want to make sure that it is most definitely the problem. For example do all the symptoms I have mentioned sound like a dying/dead motherboard or some other possible problem. And why would have the computer run with a different video card and then at Best Buy not run when a different video card was placed in?

Here are my PC specs-

OCZ StealthXStream OCZ600SXS 600W ATX12V / EPS12V SLI Ready Active PFC Power Supply

CORSAIR XMS2 2GB (2 x 1GB) 240-Pin DDR2 SDRAM DDR2 675 (PC2 5400) Dual Channel Kit Desktop Memory Model TWIN2X2048-5400c4

Intel Core 2 Duo E6600 Conroe 2.4GHz LGA 775 65W Dual-Core Processor BX80557E6600

GIGABYTE GA-965P-S3 LGA 775 Intel P965 Express ATX Intel Motherboard

EVGA 320-P2-N811-AR GeForce 8800 GTS 320MB 320-bit GDDR3 PCI Express x16 HDCP Ready SLI Support Video Card

The only way to answer your question is to do further diagnostics on your computer.
There are a lot of components within a PC, it only takes one to fail.

Do you have and know how to use a digital volt meter?

I do not have one nor do I know how to use one. The first thing I was going to do, was buy some new thermal paste and reapply it. It seems like alot of times that is the issue and it is such a simple and cheap fix. After I try that, I am clue less what to do next, besides trying to buy a new mother board as Best Buy told me. I would probably try to buy the same one I already have. The other day though, I took off the processor fan and just took a look at the processor and the paste and what not and when I tried to reattach the fan, I literally broke all of the push pins that hold the fan into the motherboard. I guess there was something I wasn't understanding about doing it, but those things are impossible. Is there anywhere I can buy some new ones online? Also I read about using some kind of bolts instead, where would I get those and how do I do it?

Have a look on ebay for things like that. Will save you money too!

Just bought the Arctic 5 silver thermal compound from NewEgg, just gotta find some pins, and I'ma try it all out when it ships.

Cool, let me know how you get on! :)