PowerBook G4 doesn't turn on every time

I have a 15” G4 machine (1.5GHz) in mixed condition and try to fix it. It lacks the battery, but otherwise everything seems to work in it. Except that I cannot turn it on some times. :) It mostly works like this, I’m not sure it is a real pattern or just I tend to recognize it: After the machine was unplugged for half a day or more, plugging the charger in and reattaching the keyboard foil to the logic board works for a few times, I can turn it on, everything works, and remains working until I restart or turn it off. When I do that, it won’t react to power button anymore. No matter how many times I reattach the keyboard or the charger.

Things I’ve checked:

• the charger is a 45W unit, but works fine with my other laptops (17” PB, 12” iBook)
• moving, rotating the charger doesn’t help
• bought a cheap similar unit for parts only, exchanged their keyboards, but the problem persists
• no fan noise or lights came up, so the logic board is not powered when I try
• tried to turn it on without the keyboard by shorting the power pads on the logic board. Didn’t help.

Has anybody a clue how to fix it? What should I check? I’m not expert and don’t have other tools than a multimeter and screwdrivers, but try to do my best.