Vijay,
Thanks again for your help.
Before I start, I'll add that I can open these files from within Excel, just not from Explorer. I have tried with several different files that worked before I installed 2013.
Anyway, in order:
Option 1:
There's nothing in this folder except a folder titled "InfoPathOMFormService", several DLL's, one XML, EXE, HTML, and VBS file.
When I search the Program Files (x86) folder for "Excel" I don't get any EXE files.
However, when I search Program Files I find a shortcut to Excel in "C:\Program Files\Microsoft Office 15\root\vfs\Common Programs\Microsoft Office 2013". The shortcut, however, is not functional:

The properties lead me to this location, where there is clearly no Excel.exe to be found:

Option 2:
I tried that while I was waiting, based on results from a web search.
Option 3:
The only third party utilities that I can think might interfere would be Norton Internet Security ver. 21.4, but this has not caused problems with Office previously. And, as I think I said, this problem has only come up recently. From what I have read online,
other users experiencing this problem used Office 2013 for a while with no problems, and all of a sudden, problems cropped up.
Option 4:
Tried that also.
Option 5: Based on the problem with the shortcut mentioned in regard to Option 1, yes, I probably have shortcut problems, though this does not affect ANY MS Word files created previously from opening. Even files I created in Word XP open fine.
Option 6: Next time I have HOURS to review all the links he refers to, I will try that. It would probably be quicker to re-install Office, but 1) since this was an install my employer requires, I am not sure how it will affect my personal files on my home
machine (I paid for a personal version); 2) Although I backed up all the customizations I could, I know I will lose some, because MS always does, such as template personalizations, etc. (such as the STUPID fact that if I close a file in Word, it closes the
whole program, instead of just the file, as in versions earlier than 2007).
Option 7: IE is current, and before I did anything, I uninstalled the Compatibility package (see above). No change.
Option 8: I guess I will. Sucks that this transition has not been smooth, not to mention other annoyances (really bad display quality, change to text boundaries in Word, and other steps backward). WASTE OF MY TIME.
Thanks for all the time you've spent, though. I hope you're getting paid.