Open it up, and check the connections from the power supply to the motherboard. Then, remove the graphics card and clean the contacts, with a pencil eraser (On PowerPC Macs, or at least PowerMac G4s they won't turn on if the graphics card can't be found.) If that doesn't do it, try this, its the fix that seems to fix my PowerMac G4 MDD when it gets a little flaky. Make sure it's plugged in, then remove the graphics card. Put the plastic air shield back in, and press the power button. (It shouldn't turn on) Then while it's still plugged in, put the graphics card. If it has anything in common with my PowerMac G4, it should turn on if the second the graphics card is put in. If it doesn't, put the thing back together, then try ant turn it on. If you still have no success, try and reset the PMU. Hold the power button down for about 10 seconds. If you still have no luck, you may have a dead power supply, of logic board.