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Intermittent power problems, in my experience, usually stem from the PRAM battery on the motherboard going bad. They are cheap and easy to replace, and available just about everywhere that sells computer parts.
http://eshop.macsales.com/item/Newer Technology/BAA36VPRAM/
One thing you can try is resetting the PMU (actually, on the B&W G3 it's called the "CUDA") on your machine -- perhaps somehow the PMU (er, "CUDA") got corrupted. To do this follow these instructions:
http://docs.info.apple.com/article.html?artnum=86760