Ooh! ooh! me! me!

I had a Dell Inspiron 8000 that was doing something very similar. Symptoms were it would power on, CD drive would reset laser motor, HDD would spin. Then a few seconds later - power off.

Sometimes it would work fine, sometimes it wouldn't work at all. Sometimes it would just turn off the display it seemed. Pressing the power button made it hibernate normally though.

Turns out the problem was a reed switch inside main section near the touchpad. There was a magnet in the LCD/lid that the laptop used to detect when the lid closed. The reed switch had broken, and the two metal fingers inside were contacting sometimes which made the laptop think the lid was shut - so it turned itself off.

I was pulling it to bits in a car while being driven to a customer's factory in Korea when I discovered it I think. One thing that seemed to fix it sometimes was flexing the case a bit. It flexed a fair bit actually.

Very different laptop of course, but it's definitely worth a shot. It's a fair bit of pulling apart though. First stop would be pulling out the keyboard (K screws on the back). The then P ones for the touch pad.