Thanks again to Mr. Belvedere, agomes and johnnydavidson, for your responses. They were of great help.
I believe my problem is solved. I was reminded by a friend that I should have a disc in my "box-of stuff-computer-related-that-I-never-throw-away" that might have come with one of my old drives that one of my sons put in. And glory be, there it was, a Nero 6.
I installed it, examined it for, what seemed like years, and was able to finally reburn one of my disks in the "Make Video CD" mode and gosh, it really worked. I was able to play it in my DVD player. I had erased the disc after copy/pasting it to one of my external drives. It just happened, I suppose, that these vids were of the type that happened to work. I'm sure that not all of my collection will. But, that's OK.
After reading the info from all of you, I had gained enough confidence to try it.
In the erasing section of the Nero, it gave me two options to erase. Full-erase and quick-erase. I chose the full-erase. Is that really necessary, or will a quick-erase also work?
Oh, and I did not see a entry about an option "single session, closed disc", but the way the "Make Video CD" worked, it came out "finished". Or, at least it worked.
The complete download was 108mb added to my C-drive, which is only 40 gigs and about half-full. I wasn't sure if I could put Nero 6, on an external drive, or not. I thought there might be a problem.
My PC is 4-years old and I'll be replacing it down the road. Then the new one will have a DVD burner-player. Course, I'll have to relearn new software, but maybe I'll get lucky and have Nero on it.
So, many thanks to you all.