Sounds like a power supply problem. I see you've tried a DVD and external drive with no luck. But it may be worth pursuing it a little further...
First, have you zapped the PRAM (boot while holding down command, option, P, and R; keep holding them down for 3 chimes)? Can you boot into Single User Mode without it shutting down? Hold down command and S while you boot. You could also try booting into FireWire Target Mode (hold down the T key while booting) just to see if it stays on; Target Mode bypasses all the operating system stuff, so it's a good test of something like the power supply.
If it shuts off in SUM or Target Mode, then it's likely hardware. Especially since it followed a power outage, which could have affected the power supply.
If it does run in SUM/Target Mode, then maybe you should try resetting the NVRAM: boot into Open Firmware by holding down command, option, O (that's an oh, not a zero), and F while booting; you'll get a white screen with black text. Type "reset-nvram" and Return. Type "reset-all" and Return, whereupon the computer will reboot itself.
If you do get it going again, make sure you have the most recent firmware. If you reply back, we can tell you how to check it.
I've had some G3 iMacs do this in the past, but I can't remember the resolution; I think we just got rid of the computers, as they were pretty old by then and not worth fixing.