I have an iMac G3 (400 MHZ, 64 MB, 20 GB HD) that when I attempt to turn it on, the only response is the sound of the monitor trying to turn on. The power button does not even light up. Before that, it would power on without the usual mac sound, but instead, a beep with the power button on. Then it progressed to this.
Your internal memory battery may have died. Check this site for battery part numbers and sources.
Mac PRAM, NVRAM, CUDA/PMU & Battery Tutorial
http://www.geocities.com/texas_macman/pram.html
Cheers, Tom