iMac late 2012 27" won't chime, boot, or illuminate screen

I restarted my iMac today from the Finder and it did not come back to life. It feels like it's permanently asleep, perhaps stuck in Target Display mode.

I had been trying to get my late 2012 iMac 27" to go into Target Display mode today with no success. I would hit command-F2, and it would switch away from the host OS video signal but not receive a signal from the connected laptop. Prior to today I would usually succeed going into Target Display mode but sometimes I would have to try twice. The first time I would see a black screen, and the second time it would operate as a second monitor as expected.

Now when I hit the power button power is delivered to the USB ports but that's about it. (I can tell the peripherals get power because they have lights.)

I tried:

• Disconnecting all peripherals, then hitting the power button
• Unplugging and waiting to reset the SMC, then plugging in
• Powering on with command-option-p-r to reset PRAM. I never get to the chime so this isn't working.
• Powering on with option held down to get to
• Removing and re-seating the four RAM chips, then powering on
• Starting up without the RAM installed to hear the loud bleeps, then restarting
• Starting up without the RAM installed, then plugging in the computer while holding down the power button. Fans spin and and the bleeper bleeps, but nothing else happens.
• Removing the RAM and starting up with only one RAM chip installed
• Removing the hard drive hoping to start up to a screen saying no hard drive could be found. Nothing happens

I never hear a chime, see any screen illumination, or see any messages on the screen.

It seems so odd that this would happen all of a sudden when I tried to restart the computer. Other than my intermittent lack of success with Target Display mode, I had no sign of this failure coming. It doesn't appear to be related to the hard drive because removing it did not change its failure state.

Is there anything else I can try at home before I either bring it in for service or sell it for parts?