Randy – I’m back in business, thanks again for your help!
FYI – the problem was possibly caused by doing a bulk upgrade of several plugins, including backupwordpress, in a situation where the upgrade of backupwordpress failed because I wasn’t running a new enough PHP. (Actually, I was, but a configuration error had it reporting as 5.2 not 5.4.) That’s just a guess, though. But coincidence or not, from now on I upgrade my plugins one at a time, so I can see the error messages.