Find the little button on the logic board that resets the PMU. Press it once, it should come right back up. If not, you may be looking for a new power supply.
I work at a university and we get this sometimes with the older G4 powermacs. I'd take the ram out, reseat it, unplug the Powersupply from the logic board, and remove the backup battery. Usually after this, and leaving them sit for a while, (few hours to a few days), they usually come back to life. I know dumb solution, but it works.
and I meant to leave the mainboard completely powerless while it sits. Not just unplugging it and plugging it back in. also, if not obvious make sure the PS is unplugged from the wall while your are doing all this.