I would try removing the PRAM battery to see if that makes any difference. Some Macs will boot fine without one.
Did you try a PMU or SMU Reset? I forget which one that particular model uses, but they are identical on how they are performed. You need to unplug the computer & press the PMU/SMU button one time for less than a second. If you happen to press that button more than a second or more than one time it will cause problems. I always used to like to use a nylon stick to press the button so I could feel it move....a fingertip makes it hard to tell if the button was actually pressed. I think those iMacs may have had two different buttons (they look the same & I forget what the other button may have done). The PMU/SMU button should be accessible with the access door removed IIRC, but it was 20 years ago....the button may be a bit awkward to reach.
Those iMac G3 Power Analog Video Boards were always failing even back in the day. More than likely that board will need to be repaired. Be very careful with that iMac cover removed because that large capacitor and FlyBack Transformer can kill you....even the CRT can kill you (the CRT can even build up a charge even when the iMac is unplugged). Those components can hold a charge for hours even after the system has been unplugged.
