The thing is, my second user could log-in, and the system seemed to be functioning for them. My question really is, what could have gone wrong for the 'broken' user - which files does login use that would produce a 'system is broken/ reboot' message? - and could I have fixed this issue elegantly?
(In the middle of running the upgrade I had had a warning that grub had encountered a problem and I might not be able to boot the system (at all) - at which point I would have stopped the install if I could, but there was only 'ok' and 'next', or similar, no 'cancel'. So I was kind of glad that anything worked really.)
In the end I was able to copy broken-user's files to a new-user, who could log-in - and use all the files...