Hi,
I have 6 or 7 of these in various models/colors and the one thing the G3 was very bad at was starting when the PRAM battery went dead.
You can usually get it running again by resetting the PRAM chip on boot. Hold down the following keys at or before you hear the chime (you do get a chime? or just a pop from speakers?) OPTION - COMMAND (APPLE) - P - R
Keep them down until you hear chime 2 times then let them go.
If no chime, but just a pop from speaker, then power supply would be next stop. If the pop is coming from inside, then you may have a more serious logic board issue.
Mike