OhmyGod,
IT WORKED!!! I've now got Mavericks on this computer, and everything is as I left it!
It took a while and once I was worried: it seemed to get stuck on "one second to go", so I used another computer to look that up, and it seems to be fairly normal.
Then the Actual Installation took place, which took about an hour, but with my heart in my mouth I logged in and HEY PRESTO!!
The first thing I did was to download a Firefox update, and the second thing I did was to go onto my bank's online banking, and WOW, it WORKS!!!
Phew. Thanks to all who joined in this thread.
