I think the DC-in board on mine is dead/dying. Charges intermittently and rarely, if ever, turns on.
My PB's would short out and make the adapter cut off temporarily. I need a new logic board because mine randomly locks up. I also need a new top case because my trackpad is dead. My battery will not work unless you squeeze it and any movement after you get it to cut on and stay on will make it cut off. I do not have a power adapter for it because when I was using the one for it with my PB the wire melted when the DC and Sound Card shorted out. It smoked and sparks flew near the adapter end. If it did this while I was not home I would be out a house and PowerBook.
Does the fan run full blast when it does not cut on?