After a lot of installing, removing, re-installing other stuff, removing it, and then re-installing Windows, there was a lot of junk on the old PC. A lot. Like a couple of Windows.old folders. One was "Windows.old.000" containing 165,642 files that totalled around 17 Gb. Not a misprint.....really big folder. As a normal user login, I couldn't get permission to touch it. As my secret hidden administrator account, I still couldn't delete it.
Some searching on Google revealed a very useful trick for situations like that. Just log in as the administrator with its elevated privileges (the usually hidden one) and then simply rename the offending folder as "$Recycle.Bin" (without those quotes) and Woof! It's a gonner. The whole several many gigs of it.
A prudent follow-up to that is to do a defragmenting of the drive. In this case, there were literally thousands (around 4,800) fragmented files to sort out. After which, your nice old computer should respond easier and hopefully a little faster.
This, however, can cause another problem. If you're a Windows Insider, and you remove those "Windows.old" folders that really aren't much practical benefit anyway, then that's going to cause your Windows Insider status to be changed from normal to one of seeking to terminate that status. And the only simple fix for that is to just go ahead and sign out of the testing program, then do a reboot, and immediately rejoin it again to once more have the desired options showing in your Windows Updates page in Settings. There's apparently no other easy cure for that problem. But quitting the Insiders program and re-joining fixes it. I know, because I did it this morning, and as I write this, the latest Win-10 build 10547 is preparing itself to install.