Thank you, bigpaws, and sledgehammer! That's worked (though I confess I don't know why), and I'm posting this having successfully connected to the net on the new system!
There's just one little niggle. The laptop has a 14" screen, which is damaged, thereby making it very difficult, in places impossible to read. However, with the previous similar laptop, I have been used to plugging in a 19" screen I have, and this has worked well - once VL is up and running, just close the laptop lid and everything used to display beautifully on the 19".
This time round, however, I'm getting the 14" display showing in the top left corner of the 19" screen, ie covering about 3/4 of the screen, but I want it to enlarge to the whole screen.
[Edit] I've asked this screen question in a different thread.