i've been looking up common problems for this model and it looks like something on the monitor frequently overheats, melts and shorts.
a quick fix is to unplug the monitor but i have no idea what all these wacky mac cables are!
it looks like the videocard is built into the back of the screen?
This is called the flyback
relay transformer! or something if I remember correctly, a pretty common problem. But this should still result in a chime, click, something. Try holding down the interrupt and/or reset button in the port bay on the side, then powering it on. If it chimes, then just shuts off, its the flyback
thingy transformer, which is like $60 to replace (and $60 can buy a new G3 iMac).