This powerbook doesn't turn on every now and then, regardless of how many times you press the power button. I've found fiddling with the memory resolves the problem, but it comes back.
Steps to solution:
1. Remove Battery
2. Remove RAM Cover
3. Swap memory modules
4. Close it up
In general, you may have more than one screw, or only one memory module. I have faith you can figure it out.