Windows resurrected overnight by mysterious forces

Yesterday evening, my Windows 8.1 system started going to a dark screen immediately on my signing in. I was able to open some individual screens on this dark background, but no features of the normal screen were accessible. Rebooting and shutting down didn't correct the problem. I found and ran a routine that cleared out the few programs I'd recently downloaded, but that didn't correct the problem. Then, sometime overnight or early this morning, when I wasn't using the computer, something put things right, and signing in brought me to my desktop in the normal fashion, where I found a window produced by some system that claimed to have fixed things for me. What could have brought all this about, and can I rely on it to happen whenever I screw up the computer?

Could you describe what that window looked like and the exact wording that claimed to have fixed things for you?
Too many questions here.
Suggest you run full scans with your antivirus and malware programs.

When I signed in, the window went dark, as though the computer was sleeping, although screen brightness could be raised and lowered a bit. Alt+Ctrl+Del gave access to some on-screen controls, including the power button. So I turned off the computer and turned it on again a few times, to no avail. In the morning I tried all this again, still to no avail. Then while I was at the breakfast table, the colorful "tile" screen returned, and thereafter all was normal again. The first desktop that appeared contained a small ad for some medicinal software, whose name I didn't note. I did not want to download whatever it was, since I suspect some stuff I'd downloaded earlier may have caused the screen problem. In fact, there may have been no connection between this window and the computer's recovery.

Now it's later that same day, and I tried to download a malware detection and eradication program, which brought with it some Yahoo stuff and some Norton stuff, neither of which looked like what I was trying to download. So I uninstalled both of them as best I could. Shortly thereafter, the dark screen problem returned. BUT, it just happened that David Pogue's missing manual on Windows 8.1 arrived in my mailbox at that moment, and within 15 minutes it had yielded a possible remedy. That consisted in acquiring the power button onscreen and selecting Restart, while holding down the Shift key. This brought up some troubleshooting choices, including Refresh the computer, which has got me up and running again. I do have to download a Windows Office package again, but I intend not to be downloading anything else for a while if it's going to discombobulate the computer so much.

You were victim to a virus/malware attack and the shift key + restart option then the Refresh was the best thing to do.
When you download anything in the future, go to reputable sites and use Custom Install to control what will be installed, never use Express Install.
What antivirus program are you using? If you still have traces of Norton in your system, us their removal tool to uninstall it:
https://support.norton.com/sp/en/us/home/current/solutions/kb20080710133834EN_EndUserProfile_en_us

Keep record of your Windows 8 key. You could also download and create a Windows 8.1 ISO and burn it to DVD or USB stick. http://www.eightforums.com/tutorials/18309-windows-8-windows-8-1-iso-download-create.html

With the Windows ISO you would do a Clean Install:
http://www.eightforums.com/tutorials/2299-clean-install-windows-8-a.html