21.5" Mid 2011 won't start.

I have an out of warranty iMac that won't boot at all. With the power cord plugged in I have led 1 lit. When I push the power button led 2 lights for 1 second. The fan winds up, the optical drive initialises, and then it completely shuts down. There is no chime or anything else. After it shuts down all led's are off, and I have to unplug it and plug it back in to do anything again.
I've tried resetting the SMC. I've reseated and tried different memory. I've pulled completely disassembled and checked connections.
I'm sure at this point that it is a hardware issue. I'm just not sure if it's indicative of a bad power supply or logic board.
Again it's not covered by AppleCare, so I would like to see if I can resolve the issue DIY.

Any help or input is greatly appreciated.

It does sound like a failed power supply. Go to the ifixit web site and you should be able to get instructions on how to check it and change it out. You did not say where you're located at or I would give some suggestions for obtaining parts. Usually eBay will have what you're looking for, and of course you could always take your iMac to an Apple store or an authorized Apple service for repair.

The ifixit web site: iFixit: The free repair manual

I did a tear down on it, and tried booting with basic config. It still wouldn't boot with just the logic board connected. I found a psu for $40 and ordered it. I'm not familiar with using a digital multimeter to test the psu. I live about 2 hours from Chicago. The $40 part was by far the cheapest I have been able to find the psu.
I also tried booting with no memory, and received not error chime.