And indeed it was Amos' wife, a genius who's a professional Mac consultant, who fixed this for me in a breath. She told me to take out all the Preferences on to the desktop and restart; if I then had sound, I should return the Preferences to their proper place in bunches, testing the sound between each bunch.

The villain proved to be the iTunes prefs, which I thought I'd already trashed.

If anyone (rich, preferably) needs a super Mac consultant, you know where to find one now.