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.