Got 'er backed up!!
I put in a CD-R disc and Windows brought up a window I'd always ignored before. I chose "format" and it did it within seconds. Then, I just dragged and dropped my major file folders. All done. Yay! I had never realized, since I had just depended on Nero, that the disc had to be formatted first, although I should have known. D'oh!
Thanks for all the suggestions. I still may get a thumb drive. There's this one image file it wouldn't copy because it was too big for the disc (with the rest of the files already there).