mid-2011 27" iMac won't turn on
EDIT 2:  Very strange addendum here.  This issue began again a few weeks after posting this answer.  BUT, I just discovered that while I have inconsistent problems manually getting the iMac to boot, a scheduled startup works perfectly fine, every time.  Go figure!

So this is totally weird and I can't explain it but...

Unplugged the mac before I went to bed last night.  Came in this morning and tried firing it up before I remembered it was unplugged.  Spoiler alert - it didn't boot.

Remembered about an hour later that it was unplugged.  Plugged it back in and just like that, normal boot!

Plugged all my peripherals back in and it's like nothing ever went wrong.  I have absolutely no idea whatsoever what actually happened but, I'm back up &amp; running.

So if by chance you're in my same boat, try letting it sit completely unplugged overnight and see if you have a similarly miraculous solution appear.

EDIT:  Some additional information I just figured out over a month later that is related to this:

Shortly after "solving" this issue originally, I realized my UPS (Uninterruptible Power Supply) was crapping out and no longer holding a charge.  I suspected this was related to my problems so I ordered replacement batteries, swapped them out, and all has been good.  Until this morning.

I woke up and once again, my machine was in a hosed state.  Wouldn't power up at all, no matter what I did.  This time even letting it sit several hours unplugged, changed nothing.

Finally out of desperation, I decided to unplug from the UPS (which was still running and showing 100% battery) and plug into the wall directly.  Immediately, the Mac booted up fine.  No problems at all.

I shut down, plugged back into the UPS, and... nothing.  No boot, at all.  So I shut off the UPS, waited 5-10 seconds, and turned it back on.  Just like that, the Mac booted up again fine!

Moral of the story here is, if your Mac won't boot and it's plugged into a UPS, try power cycling the UPS itself.  Might save you a lot of headache.