DON'T GIVE UP HOPE....My son's PS3 (fat 80gb model ) did the same thing.

To fix it I tried cleaning it out, hooking up my PC power supply to the PS3 to rule out overheating/bad power supply.
Neither was the problem....So I bought a heat gun set it to low and reflowed the chips (40 seconds each on low heat 750F).

THAT was the solution it now LIVES again.

If you have never reflowed a board then there are plenty of tutorials on the web for doing this to the PS3.
The most difficult part is the stripdown and putting back together of the PS3.

The chips solder getting cracks and needing to be reflowed seem to be the main cause of PS3 failure. Luckily it is EASILY fixable.