Put your ps3 into recovery mode. Have it turned off, and your tv on the correct channel to see your ps3. Hold your finger on the standby button to turn it on, keep your finger there until the console turns off.
Wait a few seconds, press the standby button again and keep your finger on it, you'll hear a beep as the console turns on, then two quick beeps. Lift your finger off the button. You should have a message on screen telling you to connect the controller and press the PS button.
Do it. The recovery menu should be displayed, the options you need are. 3.
Restore file system then 4. Rebuild database. A ps3 shutting down like this means it's encountered an error or overheated.
As you seem to have eliminated the overheating problem, corrupt data seems more likely. BUT When keeping a ps3 cool, it's most important not to have the console on a carpet or soft surface and that the back of the console has room, as this is where the air escapes.
I'm having precisely the same issue right now, with an 80GB original ps3. Hesitant to try the above incase data corrupts etc..
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