iMac Won't Boot Any Disk — Keeps Restarting
It's definitely a hardware problem — either the system board or the video card.

I took the iMac to an Apple Store today. It actually passed all their in-store hardware tests, but the technician still couldn't get it to boot and agreed it was a hardware issue. He'd never seen a problem exactly like this before, and said there wasn't even a standard Apple repair code for it.

Fortunately, it's still covered by Apple Care and they'll fix it for free — they said it should take about five days to get parts and perform the repair.