The computer is not turning on.

I don't know if this is your problem but there were some iBook G3 and G4 machines that had problems with broken solder joints between the graphics chip and main logic board.

the symptoms usually included random crashes with the screen going blank and the fan suddenly turning on full - or you'd get these sort of symptoms and lockup when trying to boot the machine. I had one of these machines, it would sound like a jet engine when this failure occurred.

you can google something like "ibook g4 graphics problem" and find lots of similar reports, like this one. read the article for more details.

do the symptoms sound like your problem?

if this is your problem, applying pressure in the correct spot on the case will re-establish the broken connection and possibly allow your iBook to boot. Some people solved the problem by inserting a shim inside the case, to force the graphics chip to make contact with the logic board. others have reported success in resoldering some pins (some people report other chips than just the gfx chip being the problem)

you mention some additional symptoms I've not heard associated with this problem, but it's probably worth you trying the squeeze-the-case idea mentioned in the article