this was a problem with your 'PMU'..
occurs freqently when there is a power disruption in your area..

there is also a small button on the logic board that would do the same thing.

On my machine, at least, this is called the "CUDA switch." Search Apple help for more information. Reportedly, pushing it more than one in a power cycle will render your computer useless!

I have a G4 Quicksilver 2002 that almost never powers up from a cold start -- I always have to open it up and hit the CUDA switch. From what I've read, it's a problem with the logic board or the power switch board, and would have been replaced under warranty had the problem shown up soon enough.

Try a new clock/PRAM battery--you can get them at Radio Shack.

If that doesn't fix it, it may be a problem with the front panel circuit board.