Greetings All,
Many thanks to those of you who took time to reply. After trying several of the suggested solutions, I finally gave up and took my Mac back to the Apple Store with me this morning for my third One to One session. Today's trainer said he had encountered the problem several times recently with other people's computers, and that he had had mixed results with fixes.
Since he was the third trainer who had tried to resolve the problem, and suggestions offered by in-store geniuses had not worked, he contacted Express Lane while I was there in the store and used my dismal repair record and his employee ID to get the case bumped up to Tier 2.
They looked my computer up by serial number and determined that the iLife software that came preinstalled on my Mac was not listed in a particular folder. They deleted that folder; when it reappeared, so did ALL of the appropriate software, including iPhoto and GarageBand. We then went back to the App store, and everything updated without a hitch.
I am sorry I can't be more specific about the name of the problem folder or where to look for it. As I mentioned, I am very new to Mac and just beginning to learn my way around things you probably all do in your sleep. The trainer and Express tech resolved the problem, but they were talking and clicking away faster than I could keep up.
If anyone else out there is still wrestling with this problem, hang in there. It may take patience and dogged determination, but the fix you need is out there - and life gets a whole lot simpler once you find it.
To the in-store trainers who didn't give up: Thank you!
To the folks behind the curtain at Apple: There is a problem here. Please fix it so others don't have to spend countless hours banging their heads against the screen and wishing they'd stuck with a PC.
Thanks again to Kukzee, elango1, and Dah.veed (to whom I also owe an apology for not being able to find the bullet point to spell his name right. As I said, I am embarrassingly new at this. Please forgive me. 🙂).
Be well, all, and happy computing.
Jefraize