Looked online, found info on the four LEDs indicating power supply and motherboard functionality. Long story short, after being strung along and lied to for 8 days, I finally gave up and went back to pick the machine up. No appts available for a week at the local Apple Store, so I took it to Microcenter, listed as an Apple-authorized repair center. Haven't worked on one of these before, and being a critical machine, preferred not to start experimenting. (I subsequently discovered that the same click occurs if the drive is connected, and the iMac is first plugged into a power outlet, so apparently the drive is reacting to power that is present on USB whenever trickle power is present, even with the system off, and the power button depressed for 10 seconds must result in a momentary interruption of that power.) Pressing the power button on the back, either momentarily produced nothing - no chime, no display, no fan - no indication of anything at all, except a USB-connected superdrive would make a clicking noise after the power button was held for 10 seconds or so. For a moment I wondered if I could have moved the cursor into a hot corner that just shut down the display. No noise or anything when it shut down, just the main display, and an external display connected to it, suddenly went black. I have a Late 2013 iMac 27, which has been trouble-free since I bought it at the very end of 2014, until two weeks ago, when it spontaneously shut off while I was using it, and then could not be restarted. One line summary: imac spontaneously shut off while in use, won't power back up at all, doesn't seem to be the power supply, so what is it likely to be? Hoping somebody here can help with ideas on what might be wrong.

Late 2013 imac hardware