Whew! I did it! I didn't/couldn't do it the way you said, so I did it "the hard way." That is, I went to the Zotero program on my old laptop, clicked the little wheel that says "Actions" and chose, Export Library. A whole bunch of files were exported to a file on my laptop. I copied that onto an external memory chip and plugged the chip into my new PC. For some reason, I couldn't copy it, I kept getting messages while it was copying so we gave up on that. Instead, I used the chip and read all the folders, about a hundred of them probably, each referring to one of the references. Inside each folder was one file with a firefox emblem, excuse me, icon. That was the key file. I clicked on that and the reference I wanted popped up in my new computer in the Zotero section. Then, I saved it to Zotero, just as if I had taken it from the internet or something, took a "Zotero picture", and then went onto the same file. It took about an hour, and I'm sure there is a better way out there somewhere, but anyway, this did work.
So, thanks for being there and giving all the support along the way. I'm still trying to figure out how to get my .wab file from my old compie onto the new one, but that's on another thread somewhere, I think!
Many thanks to all.
Dr. D.