Somebody gave me a PS3, and when I power it on, (From no light to red light) it stays on. Then, after I push the power again, the light changes to green and I can hear the disk start to spin, and then power goes off completely. But here's where it gets odd: Sometimes it stays on for 3 seconds, sometimes I can play for an hour or so, and sometimes it gets as far as the PS3 intro screen and then shuts off.
Also, when I first got it (from a friend), it had a game stuck in it and I had to open it up to remove the game. Right after I took out the game, it worked fine for about an hour. If this helps, I have the 3001a series with no disk light.