Might be time to replace the PRAM Battery, 4 years is close to their lifespan, far less if ever without AC power, & can cause strange startup problems...
See which one your G5 has...
How to reset the SMU/PMU on a Power Mac G5 (Late 2004) or Power Mac G5 (Late 2005) ...
Earlier G3, G4, G5 models...
Troubleshooting: My computer won't turn on
Resetting the Logic Board
Resetting the logic board can resolve many system problems. Whenever you have a
unit that fails to power up, you should follow this procedure
before replacing any modules.
1 Unplug the computer.
2 Press the Power On button on the front of the unit.
3 Open the side access panel.
4 Remove the battery from the logic board.
5 Wait at least 10 minutes before replacing the battery.
6 Make sure the battery is installed in the correct +/-
7 Reassemble the computer and test the unit.