Sounds to me that it might be a video card problem. I had a similar problem the PC would work for a while and then shut down. I suspected it was the card. When I took the card out, although the fan was running, when I rotated it by hand it was a bit stiff. I assumed the video processor was therefore over heating. A direct replacement was out of stock at the time, but I was able to buy one with a better spec. at the same price. My new card had a large heat sink in place of the fan. Replacement was relatively easy, the main point to note is to make sure you discharge any possible static electricity by earthing yourself before opening up your PC or taking the new card out of it's packing by earthing yourself. Boot up and install the video driver.

In the past I have used my local Computer shop and gat service at reasonable rates. I would avoid the big computer stores like the plague. Tey will fleece you.