OK, now I’ve figured it out somewhat. The problem with my custom widgets started when I did a manual update of the WordPress Tarski theme to version 2.4. Before doing that, all my custom widgets appeared in my blog. However, after deleting the old Tarski files and then replacing them with the new 2.4, all my custom widgets vanished from my blog. If I use any other theme besides Tarski, they won’t show up at all.
I did check out the Tarski support forums, but couldn’t find much useful advice there. Guess I’ll have to write a new post to the authors about this. It’s strange how only Tarski 2.4 allows my custom widgets to be seen. Or perhaps I could or should revert back to an earlier version of Tarski and see what happens. If anyone has any ideas or suggestions please let me know. Thank you.