Sounds like your PS3 is overheating, and has been for a while. It's likely beyond repair at this point unless you have it professionally reballed (which will cost as much as a new motherboard).
original 60GB PS3s have overheating issues for a couple of reasons:
1) The paste beneath the heat spreader on the Cell and RSX is very low quality. Replacing this on the RSX is fairly easy (the heat spreader can be carefully removed, cleaned, and attached with better thermal adhesive), on the cell, it's almost impossible without the right tools, as they put some heavy duty epoxy on like 90% of the perimeter.
2) The heat pads on the RAM and Blu-Ray chips dry up and become useless after about 4 years.
3) The PS3 while playing PS2 games runs the fan at at flat 25%, which is far too little to dissipate the heat the Emotion Engine, Cell, and RSX produce. Your PS3 is running at around 85-90C within 20 minutes.
4) The default PS3 fan profile doesn't ramp up the speed of the fan until after it is already 82C, and runs high until it goes under 76C. This means every time you turn on the PS3, it's getting very hot, then getting cooled down by the fan rapidly. This causes the mainboard to flex a lot.
If you DO get it fixed, I highly recommend getting it hacked just so you can adjust the fan profiles so it activates at 68C and maintains that temp and runs the fan at 42% in PS2 mode.
Anyways, just get a PS2 and a slim PS3. It's not worth the trouble with the originals. I've taken very good care of mine, replaced the adhesives, pads, and pastes and have had the better fan speeds on it for a couple of years, and it still gets hot very quicky.
