A series of recent problems - what might be causing them?

I'll try to keep this brief, since the full version would be way too long, but strange things have been going on with my computer lately. First, some background:

Computer: Hewlett Packard Pavilion Elite HPE-112y (5 or 6 years old now, a home system)
Original Operating System: Windows 7 Home Premium
Upgraded to Windows 8 and then 8.1 and, as of last Fall, Windows 10 (via the automatically downloaded upgrade)
It had some trouble upgrading to Windows 10 but eventually succeeded and has been working fine.

Here is the quick version of the events I can remember from the last couple of weeks:

To get all-in-one wireless printer/scanner to work (which had been working before -- a HP B209a-m I think) I followed HP's suggestion to switch to private network.
I ended up having to reinstall printer driver but the installation failed as well as it's attempt to roll back the installation.
On every startup the system tries to complete the installation of the printer but cannot due to missing files.
Every attempt to install, including using HP's special installation process, failed the same way.

Windows Update did not seem to be working. Would always fail on the same update whether done automatically or manually. Has seemed to work since.

Tried System Restore but could not get back far enough to get everything working properly again.

System File Checker (sfc) reported no problems.

chkdsk reported no problems

chkdsk /R reported no problems but I was suspicious of it since it started up saying it was 100% complete and took a very short time to test a 1 TB drive.

I wanted to backup my files and do a clean install but the system no longer recognized USB external drives (or USB memory sticks). Device Manager shows USB drive under Other devices and marked with a problem: "The drivers for this device are not installed. (Code 28)" Updating the drivers in Device Manager seems to work, but the drives are still not recognized by the system.

Downloaded a Windows 10 Pro .iso to attempt a repair and tried to mount it. Mounting failed for some obscure reason.

Burned the .iso file to a DVD to try the repair. All seemed to be going well until, hours later, I get a rather unhelpful message saying "Something happened" and that Windows 10 could not be installed. (Maybe because I forgot to turn off anti-virus?)

Just this morning I noticed the Windows key no longer brings up the start menu when I press it, nor does left clicking on its icon in the taskbar work. Combinations such as Windows-R still work, as does right-clicking the icon.

Summary: The computer basically works, the programs I run still run, I can connect to the internet, etc. But I can't print or access external storage. It seems a hardware problem would bring more catastrophic difficulties so I suspect a software problem but I can't find what needs fixing and the system itself seems to be preventing me from starting clean without losing everything (Yes, I got lazy with backups).

I haven't tried everything I've learned on this forum yet, like dism /online /cleanup-image /restorehealth, and I'm not at that computer right now and can't give you the details on everything that's been happening, but finding this forum is the one good thing that has happened from all this. Can anybody see a pattern to these things? Does it seem to be software?, Hardware?, A virus?, A delayed side-effect from multiple upgrades? A progressive disease in an elderly computer?

I'd be grateful for any suggestions you can make.

The brief version I would have read.

whs said:

The brief version I would have read.

Sorry, it's my first post and I was trying to avoid having someone tell me they needed more details. Here's the really short form (details above):

Computer upgraded from Windows 7 Home Premium to Windows 8 then 8.1 then Windows 10 -- which has worked for months.

Install of printer driver failed and was not completely removed so remnants remain to fail on computer startup.

Windows update did not work consistently.

System Restore doesn't help.

sfc, chkdsk, and chkdsk /R all report no problems but I don't think chkdsk /R worked correctly

Windows will no longer recognize USB external drives or USB thumb drives -- claims no driver available even though they worked before

Windows won't mount .iso files

Attempt to repair Windows with DVD failed (maybe because I neglected/didn't know to turn off anti-virus?)

Windows key started not working, along with left-clicking its icon in the taskbar. (Windows-R and right-clicking still work.)

I'm not currently at that computer or I would have tried some other things I learned on this forum. Was wondering if anybody sees a pattern in all this and has any suggestions.

Being brief is in the eye of the writer.