Booting to black screen with working LED backlight

I have an early 2014 11" MacBook Air that boots to nothing but a black screen. The LED backlight works, and I do not have a mouse cursor.

I updated the OS to 10.13 (minor revision would have been whatever was released December of last year). I was able to boot into my account after the update, but a couple weeks afterward the computer got very hot, shut down, and I ended up where I am now.

Things I've tried so far:

- Reset PRAM (option, command, P, R). Prior to this step I had no boot chime; after this I had the boot chime. This was the only step to make any noticeable difference.

- Reset SMC (shift, control, option, power)

- Try to boot to System Recover (command, R). Screen was still black. Attempted to right-arrow once to the recovery partition with no success.

- Try to log into to my account blindly, hit the power button to trigger the shut down pop up, hit 'S' to select "Sleep," and then enter. Once asleep, I should have been able to hard shut down and then boot back in with a working screen. No success with this.

- Open the back cover, disconnect the power connector from the batteries, hold down the power button, and then reconnect the power connector. No success here either.

Any other ideas?

Edit (3/26/18): Correct from 10.12 to 10.13.