Here is a trick I have used for many years.
Remove the battery from the machine.
Remove the power plug from the machine.
Press the CUDA button(it is on the motherboard), little square thing with a top that looks like a pencil eraser. ONCE
Press the Power On button on the front of the machine.
Leave the whole thing for at least 30 minutes.
Put the battery back in
Put the power cord back in
Press the Power On button on the front of the machine
Sit back and enjoy the startup chime.
If this works, let me know and I'll tell yo what we just did. If not, tell me and we'll start again
I bought a used G4 and it worked OK for a bit but it used to lose the time and date.
One day, it wouldn't start at all, so I worked out it was probably a PRAM problem and changed the internal battery.
The new battery measures OK on my (admittedly very basic) meter but nothing happens when I try to power up the machine.
I have checked and there is mains voltage going to the power supply. Any ideas?