Q: iMac won't boot past loading screen

Came back to my office after a couple hours lecturing, and found my 2012 iMac (El Capitan) with a blank white screen. Rebooted it and found it cycles through to the Apple screen with the progress bar, then before it finishes, goes to black, then it will go grey, black and then usually reboot again. Endless cycle.

I tried several sorts of startups. These didn't work:

Safe Mode

Netboot

Netboot Network (sometimes gives me a spinning globe, but stops)

OS X Recovery (both regular and network)

I can boot up in startup manager and choose a boot volume, but all of my choices (bootable USB, external HD, recovery drive, time machine) end up crashing on the apple screen with progress bar.

I can boot up in single user and verbose modes. I tried this:

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Step – D. On the terminal window Type fsck –fy and press return

Step – E.  Type mount –uw and press return

Step – F.  Type touch /private/var/db/.AppleSetupDone and press return

Step – G.  Type exit and press return

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No improvement. Using suggestions from other discussions, I removed .kxt files from Logitech and Olympus I found in the extensions folder in single user mode.

I can boot up in hardware test mode (net only, I think) and the hardware tests fine, in both the quick test and the detailed test. So, maybe the hardware is fine.

And yes, I zapped the PRAM.

The computer won't boot from my elcapitan boot/install usb at all, and I'm not sure I have the original OS X CDs that came with the iMac (if any). My guess is that won't work either.

And yes, I've unplugged all my peripherals and second monitor.

Any thoughts or suggestions??? I'm on Guam and my repair options are both limited (and inexperienced).