Windows minimizing and reappearing on clicks?

Tyler, we're getting somewhere! PowerShell was unable to fix your corrupted files with sfc /scannow, but it did find out that you have corrupted files. Here's what to do:

Windows Resource Protection found corrupt files but was unable to fix some (or all) of them indicates a problem.
In this latter case, type (or copy and paste) DISM /Online /Cleanup-Image /RestoreHealth into the PowerShell window and press the [Return] key. This will download files from Windows Update to replace the corrupt ones and, again, this may take some time.

Fixed with a complete reinstall of Windows through USB obtained from another computer. I dunno if that was necessary but it worked.

I would assume it was a rootkit of some sort that was buried in the boot files, and had also infected the recovery. Reinstalling Windows the first time through the recovery wasn't enough to get it out, I had to completely clear the partition.