I had this problem a long time ago with my imac g3 333Mhz, it would chime, and try to power up, and in a few seconds, shut off, in the end, i needed to replace the board that drives the CRT, try running the computer with the internal display disconnected, i believe these iMacs have a VGA out port on the back as well. This board is hard to get to, but after a little disassembling, i got it, if you decide to try this, take a picture of all of the connections, since it was really hard to remember where every thing was connected.
"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."
and 2. Zap the PRAM(Restart, while screen is blank, hold down option, command, p and r until two start up chimes).
*try 3. Put a system install disk in the slot loading cd-player as you hold down the option key, it might show a. icon of your HD and b. the system install disk. If it does click on the sys. install disk, and find the disk utilities to try to repair permissions etc.
*try 4. Safe start, hold down the shift key when restarting. This turns off all extensions.
*asterisks means not sure if you INSTALLED SYSTEM has these options.
*Disk warrior and/Tech Tools are good disks to try to start-up on."
Quite often the Flyback Transformer shorts out. This will cause the problem. The answers above should all be tried first. I finally disconnected the video and used an external monitor.
