Thanks again, Ric.
The CD player is actually pretty old. It's German, a SilverCrest CD-Player with Radio KH 2328. I've still got the manual (more pamphlet), which doesn't say anything that I can see would be helpful. It's just occurred to me: with its being so old (could be 20 years?) would mp3 compatibility be built into it?
Regarding the burning I did on the CD: I burned the tracks mostly singly or in some cases in threes or fours. But even when I've selected a track from a batch of three, only the first one has been played and replayed.