Update on problem
Thanks, Trainableman. I tried all that you suggested, but it still didn't change the picture. However, a friend of mine came up with a solution that seems to have fixed the problem. I submit his suggestion here:
" under the "Run" command, which you will find under All Programs/Accessories. Go to Start button, click on All Programs, then find Accessories (after Windows programs in list), and click on "Run". In Run box type the following:
%USERPROFILE%\AppData\Roaming\Microsoft\Windows\Themes
A list of "slideshow.ini" files (maybe one or two) should come up, along w/"TranscodedWallpaper.jpg". What the suggestions online say is to clear all info from the .ini files (delete all characters, and there are a LOT), then reboot, then try to reset the slide show under "Personalize" feature of the desktop like you've done before - this clears out any corrupted picture files, which the online forum says is the problem, and lets you start fresh. This is less drastic than a Restore, I guarantee you, and should work... "
Now, the only thing I found when I did this was the offending picture, which I deleted. Fairly soon it started showing another picture in that series, which would have been correct, per the picture set I had selected at that point. But I closed out, rebooted, and changed my personalization settings as usual, and it seems to have fixed it. Praise be for friends!!!
Maybe this can help someone else. Thanks again for the effort and response.