White screen of death no matter what

tl;dr No matter what I do, I get a white screen on startup after the Apple logo. Resetting PRAM, PMU, Safe Mode, and booting from external drives all have the same result.

I was doing a routine hard drive replacement. The original HDD was drastically slowing down and giving SMART errors, so I replaced it with a (somewhat smaller, but still big enough for all the data with room to spare) SDD. Everything worked fine; I installed the drive, booted with a Techtool Protogo USB stick with the High Sierra installer on it, formatted the disk with Disk Utility, installed High Sierra onto it, waited for it to reboot, plugged the old drive in via a Universal Drive Adapter, and restored all the data using the Migration Assistant built into the initial startup sequence. Great! Everything was working fine. And then it restarted, and—nothing. It refused to boot after that. Not only to the new internal drive, but to the Protogo, or to the original drive, or to the Recovery partition, or to Internet Recovery. It will show the Apple logo and the loading bar, then go to an all-white screen and stay there.

Well, that's what it does now. However, last night it would sometimes do that, and sometimes go to the white screen and then shut down, and sometimes spontaneously reboot, over and over. Once it immediately turned itself back on after I forced to turn off by holding the Power button for six seconds. When I went to Recovery or Internet Recovery (after it downloaded the installer), it would go to a horrible blue screen, that looked like some kind of awful graphics error—it hurt my eyes. When I boot to my Protogo, it shows a line of random colors in the upper portion of the screen for a second before it goes to the white screen.

I have tried: Booting in Safe Mode (no indication that that took effect), zapping the PRAM (seven reboots in a row to be sure), resetting the PMU (twice), Verbose mode (which works, until it goes to the white screen of death), Single User Mode (which works just fine, but all I know to do from there is to fsck the disk, which returns no errors), unplugging the battery for 30 seconds or so, resetting the RAM in its slot, and, as I said, repeatedly attempting to boot from an emergency drive. Nothing has worked. I am at a loss. What in God's name is going on here?

Also tried: Apple Hardware Test, extended testing: No trouble found. Booting over Firewire from another computer in Target Disk Mode: No difference.

Hm. I'm noticing that the computer is getting unusually hot, roughly where the fans are (i.e. not the battery).