well the 61XX series wont boot with video without a good PRAM battery, but however the power light would still remain lit. I could get a 61XX machine to fire up without a battery by powering it up, quickly powering it off and right back up. it would then boot.

but your issue is clearly the power supply. Put your ear next to the power supply or use one of those doctor stethoscope thingies and listen to the power supply. if you hear a tick-tick. failed power supply.