Neighbour couldn't get round, he was held up sorting some other problem out elsewhere, so being a tad impatient I decided to go for rolling it back to when it last worked and then trying again. No problem with the PC rolled back, updated Norton, downloaded email, updated Windows XP, downloaded email (with various reboots in-between - everything worked perfectly.
Turned to laptop. Rolled back. Updated Norton (two updates, just like PC), downloaded email - correction tried to download email! Same problem as before. So rolled back again and this time installed one Norton update, tried email - it worked. Then one by one I carefully downloaded and installed each Windows XP update (rebooting between each one, checking email between each one and setting a mark for a roll back between each one just in case). Finally, because the worst that could happen was a tiny roll back, I tried doing the other Norton update and .... Yes, it worked!!! Why it suddenly worked, I didn't ask. I'm just cautiously relieved (I'll be totally relieved tomorrow when it is still working).
I'm exhausted after my day and it was not how I intended to spend it. So I shall now go and relax and put my feet up and maybe have a glass of wine and tomorrow I can do all the things I was going to do today (hopefully). Not to mention catching up on today's stuff.