It can be 2 things: the video card or the pci-e slot.
From the information you provided, the card is getting hot when being used. I have a 8800GT Superclocked, another hot card but I use Riva to raise my fan upon temperature reach. With that setup, my card never sees 60°. Keep in mind of the temperature of the room too.
Try booting up windows in safe mode and updating the drivers, I don't believe it will fix the problem.
No I haven't overclocked anything, gpu or cpu. And the PCIe is on auto, defaulting it to 100mhz.
Which of my part(s) of my system are the more likely culprit? And does the Microsoft Memory Test only test system memory, and not video memory? It did tell me that one of my components are failing, contact my computer manufacturer. But that's all I could get out of it. It didn't tell me which component.
As of now, I'm running XP on the same system. So far, so good. I haven't tried running on 3D yet. I did try to run Assassin's Creed once and I had to restart. The game went all trippy like, psychedelic on the profile screen. I haven't tried again since.
Hmm, also I'd like to add that back in Vista, everything game I tried to run would give me a nvlddmkm error. And the last time I tried to run WoW I got a "memory could not be read" error. Which memory was it referring to?
Sure sounds like a video card problem. The best test is to put it in another system. Since it's a new card you should contact Gigabyte and explain the problem to them and they should offer you a quick return. The white dots you see on booting up tends to point the finger at the card, though an outside chance could be a bad or weak PSU. Contact Gigabyte.