The main problems that I have come across recently with the fat PS3s is the fact that they[the motherboard] are paired with a daughterboard that sits under the disk drive. I know this because I got a second PS3 that I had to take apart. Often times, that daughterboard goes out in the fats, and to get it replaced, you do have to send it in for service. Trust me DYI service would not help as the daughterboard is "paired" with the motherboard, meaning that you can't replace it with another daughterboard without pairing the two together.
Even though the PS3 MIGHT be working on the outside, the only way to tell that you even have a problem is putting in a PS3 disk and try to get it to read.
Have you asked to test out a game on THAT PS3?