I inherited a old iMac(2006) model A1200, I've gotten it to turn on for extended periods of time, reinstalled snow leopard twice and fully updated once. Every now and then I'm able to get it to boot up but eventually it will shut off on me then I am unable to power it on unless I unplug it for an hour or more. I examined the LED indicator lights on the logic board and when I plug the power cord in, LED 1 lights up, then LED 2, then LED 3 does for a split second and it instantly powers down. Anyone have any idea what I'm looking at here? Bad logic board or bad PSU? Any input is greatly appreciated thanks!
If it's shutting down suddenly and then refusing to boot up until it sits for a long stretch, that's a classic sign of overheating. And on a machine that old, the first thing I would check is that the fans and especially the CPU heatsink aren't all clogged up with dust. See if that gets you anywhere.
It could also be a dying PSU - or also, overheating in the PSU. Particularly if the PSU's fan is not working properly. Check that also.
If neither of these routes turns up anything, then I'd guess it's time to move on to other components.