This machine had capacitor issues (all boards and even at times in the power supply.) If you must get it working maybe find a working G4 off Ebay but no shop I know will touch these.
How are you are cap replacements?
I inherited a 2002 G4 Quicksilver (no discs), when I powered it up it went to desktop and then turned off.
I replaced the battery and the same thing - it runs for about a minute and a half. The led on motherboard goes out, I tried the small reset button to no avail. I have to remove power lead for around half an hour before it will power up to give me the minute and a bit - any less time unplugged means a shorter on time.
A friend suggested there might be some kind of thermal switch.
The fans all work.
As it has loads of bells and whistles and a lot of ram I would like to use it.