So far, my searching hasn't found anything useful relating to this subject on the web. I can't be the only person in the world who wants to listen to their music in another room! It does appear to be a licence restriction though. I tried an experiment. I burnt two of the tracks that I couldn't access on to a CD. I then deleted those tracks from the library and the computer. I then copied them back from the CD into the library and, hey presto!, I could play them via the laptop through my home network.
If this is the case for all of them, it makes a nonsense of legal downloads because the licence is too restrictive. It's cheaper to buy the CD from CDWow. Perhaps I should immediately burn all downloads on to CD and then copy them on the computer from there, bypassing the licence restriction. But would that be legal? Maybe I'll open another post on that subject in consumerwatch when I've done some more experimenting.
Meanwhile, if anybody else has any experience of this, please let me know. Thanks.