I would look first at a GPU problem, which if you do not have a spare will be difficult.
Motherboard is old by PC standards and I would assume that your graphics card is also. You do not state what make of 6800GT you have but I'm thinking that having its fans clogged up with carpet fibers will not help in keeping it cool.
Try another card if you can, borrow or buy.
A lesson can be learnt here though PC fans suck in cool air as well as blowing out hot,dust etc will come in to a PC through the intake fans as well.If you must keep your PC on the floor buy some cheapo fan filters. They are much easier to clean.