Diagnostic led 1 stays on until hard drive plugged in

My mid-2007 iMac 24" 2.4 Ghz stopped working.

It would just shut down after being on for a few minutes, and eventually wouldn't power on at all.

I did some reading (big thanks to all the contributors at iFixit - such a great resource!) and learned about the 4 diagnostic LEDs inside the computer.

I opened up the machine and saw that the first LED was turning off after a while. I removed the hard drive and noticed that the first LED was now staying on all the time. Could the hard drive be drawing too much power or something? I tried another hard drive and had the same thing happen.

If I put the hard drive into a Firewire enclosure, I can boot off of it, and the computer does not shut down.

I'm hoping someone here (Mayer!) can give some advice as to what I might do to repair the iMac.

Thanks!

Update: now, led 1 doesn't stay on for more than a few seconds.

Is there a way to determine if it's a power supply problem or a motherboard problem? I'm willing to replace the power supply but the motherboard is probably more than the computer is worth.