Power Mac G4 doesn't start anymore
Battery alone? Eh, probably not. There should be at least some signs of life if the battery were dead - I would expect the power supply to come on, at least.
Circumvent button? Yep. Often, Apple engineers will leave little debug buttons or contacts on the motherboard that allow you to power it up. They might be buttons, or they could be two little contacts you have to bridge with a screwdriver.



  Note: To do that, you would have to have the machine connected to power and open. Don't touch anything inside the machine while connected to power. That shouldn't need explaining, but anyway...



Other ideas? Fried MB. Seriously. I had an iMac G5 (and I think and iMac G4 too) die of a fried motherboard, and it had the exact same symptoms. Before it died, there were some, uh, weird graphics problems. Like the volume control overlay coming up black and not going away. Stuff like that.