A little more detail on the technical side might help, including any trouble shooting you may have done. Is it plugged in? I'm not being facetious (well, only a little). If it was left unplugged for a long time your PRAM battery may be dead and that will cause startup problems. It really would help to know exactly what it does or doesn't do when you press the button on the front. Any lights at all, even for a second?
If you don't know the model, find the Serial# & use it on one of these sites, but don't post the Serial# here...
How to find the serial number of your Apple hardware product...
A little more detail on the technical side might help
We also need to know which G4 you have and what version of the Mac OS is installed. This Apple article may help on the "which model" issue:
Power Mac G4: Computer Does Not Power On, No Fan Movement
Troubleshooting: My computer won't turn on
Power Mac G4 Resetting the PMU on the Logic Board
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.
This procedure resets the computer’s PRAM. Be sure to
check the computer’s time/date and other system parameter settings