Are they both in the same room? It sounds like a power problem. Try running an extension cable from another room and plug the Powermac into it. No surge protectors etc in between while testing.
If it powers on fine, you can identify what the reason for it not powering on when plugged into the sockets in that room. It could be a faulty surge protector or socket gang.
Do you have any enerfy saver prefs set? Power on or power off at a certain time? These could be interfereing.
The last thing it seems like it could be are the pram batterys. I think the Imac g3 and Powermac g3 were manufactured about the same time, so it might be about time for replacement.
Hope this helps,
Sean