Have you tried resetting the PMU? Assuming this is a Power Macintosh G4, if you open up the side and look on the logic board, you'll see a button that is for resetting the Power Management Unit (PMU). The instructions on what to do are here:
http://docs.info.apple.com/article.html?artnum=95037
Make sure you only push that button for about 1 second....just a quick push. It's all laid out in the directions.
Also, see about reseating the RAM modules or try and get some new RAM for it.
More information on your Power Macintosh G4 (if this is what you have) here:
http://www.everymac.com/systems/appl...ac_g4_500.html http://lowendmac.com/ppc/g4saw.shtml