So, I finally found a solution to my problem and hopefully didn't do any serious damage in my previous misguided attempts to fix the problem through editing the registry.
Here are the steps that fixed the problem for me, straight from Microsoft:
Copy the following text, and then click Start and past the text into the search box and click the Enter key on the keyboard:
%USERPROFILE%\AppData\Roaming\Microsoft\Windows\Themes\
Right-click the file that is named TranscodedWallpaper.jpg and then click Rename
Rename the file to TranscodedWallpaper.old, (change .jpg to .old) and then click Yes when prompted
Double-click slideshow.ini. Slideshow.ini should open with Notepad. Select all the text in slideshow.ini if any exists and press Delete on the keyboard, and then click File and Save to save the changes.
Close Notepad and close the Windows Explorer window and browse to the picture that will be set as the background image
Try to apply a background picture again
Worked like a charm. Thanks to everyone who offered advice.