Well, here is the deal: I did use my 30-day free TS option and we opened a case number. First, we made sure that the .NET Framework 3.5 SP1 update was already installed in my OS. Apparently, not having that update from Windows can be the issue. You also want to be sure that your Windows OS updates are all up to date and correctly installed. In my case, these were all already okay.
After those confirmations, TS had me right click on the WD tray icon, and select Exit WD Smartware. Then, TS had me reinstall the WD Smartware software. This process of course reinitiates the WD Smartware to check the backup for all the files from your C drive. After that, the issue, theoretically, is fixed. We found that all was well initially.
Then, a couple days later, I saw the problem reoccur briefly, then it disappeared (so far) for good. I called TS just to be safe on my same case number. They said that based on all aspects of my case, it would appear that the issue is resolved. If it does resurrect, their tentative solution is to uninstall and then reinstall the .NET Framework software.
I just wanted to pass along my observations for what it's worth. Hopefully, this will help some folks.