This one of the most common G4 problems
Okay after extensive searching and undetermined problems of what could be the wrong with my with my G4. Steps I would try: remove any and all usb cables. Firewire cables especially, because firewire connections are known to create faults. Keyboards, mice. Open case door before power up with tower unplugged, press power button briefly and it should light up for a second then shut off. Next remove ram cards and replace only one, this will help upon pre determining possible problems. Next make sure every thing is seated correctly ram, pmu battery, Ide/sata cables, power cables, anything that looks to be plugged into something. Next with door open, plug in power cable and power on. Notice a red light illuminates on the logic board, if so you have power to the board, if no light possible power supply issue exists.
Now if your tower starts up as usual try one step elimination by connecting each additional rams, again with tower unplugged, and additional usb and firewire cables you may find that one of these items gone bad can wreak havoc for you.
Hard drive process of elimination can prove responsive to this type of problem as well, blue screen? Flashing folder image? no drives found cant read drive? Post questions or PM, let me know how you do!!!!!