IMac screen froze while in use, shutdown, restarted, got worse

Here is what you know from your excellent details:

1. The keyboard isn't working since all of the shortcuts get handled from the firmware in the Mac.
2. The Mac can't find any bootable OS X due to corruption or hardware failure

Why the keyboard isn't working isn't yet clear. I would disconnect everything including the power and then remove both RAM sticks - noting which was on the top and which was on the bottom.

Next, plug the Mac in and power it up with nothing connected. You should get three beeps indicating the POST (power on self test) detected no RAM. If you have severe hardware problems, it won't know the RAM is missing and you'll know you need to get inside to fix it.

Assuming this works, power it off after waiting to see if it boots in 5 minutes time (really wait that long for the Apple logo to show up). While you are waiting listen carefully for rhythmic noised from the hard drive. It shouldn't keep seeking past the first 45 seconds and if so - you will know the controller or the drive is faulty. It should spin quietly after a few minutes or be reading the drive if it's corrupt and the hardware / OS is trying to fix things.

Next - power it off by the button and put the "top" piece of RAM in the "bottom" slot and repeat. Lastly - if you get to the white screen at this point, try another keyboard (command-s or shift held down are the best options here for troubleshooting) to see if you can isolate the failure further.

I tried to make some assumptions about what is wrong and you can edit the question or ask another with the step that fails referring to this question if you want to isolate things further before attempting a repair.

As you have seen, all Apple products actually run even when you power them off. On iOS, the battery keeps time and on Macs, the SMC is responsible for knowing when the power button is pressed and if the Mac should start itself up due to a scheduled wake or power on being saved in the NVRAM.

If you called for service, Apple would likely focus on several things:

1. Have you checked that the firmware and software is up to date.
2. Does this happen every single time, or is it an occasional thing.
3. Have you disconnected everything (including the mouse and keyboard) and tested to see if it's in any way related to a peripheral.

Assuming you can reproduce this at will (it happens every time), you would probably take steps to reset the SMC to ensure it's getting proper readings from the temperature sensors.

• Intel-based Macs: Resetting the System Management Controller (SMC)

If after spending the 10 minutes it would take to read through each and every step (I feel it's important to perform the steps in order - even if they seem unrelated or unnecessary), I would expect them to want to run diagnostics to physically open the Mac to check the sensors and wiring. Your symptoms sure sounds like the SMC either is stuck in some loop and not reading the temp sensors. Failure to control the fans properly could also be a hardware issue where the SMC is receiving a signal where the correct action is to keep the fans not only spinning, but spinning at an elevated level.