After numerous failed efforts to fix Katie's computer without doing a bare metal reinstall of Windows 10, I finally gave up and did so. Tonight, I finally got around to configuring it, installing anti-virus software, and getting Katie set up to log back in.
Then Windows decided to install updates. Now, the computer is in the same Automatic Repair failure loop that it was before. There are two System Restore points, but neither of them will allow a restore to actually occur.