Thanks, Englishal. What I should have said is 'I've tried ICS'. It's not on now. I'm with Pipex (1mb connection).
In fact, I think many of my problems are caused by the fact that the Creative modem is a single-port router in its own right, with the ability to DHCP serve. Even though I've tried disabling its DHCP server (not easy - both the router and the modem originally shared the same IP address!), it still won't play. I've also tried setting the router into 'bridge' mode to let the modem do all the DHCP serving, but no joy there either!
As I said, what I (and most of the rest of the world) need is a box you plug in and everything works, but it seems that networking - for the moment at least - remains the preserve of those with more techno-geekishness than I posess! Frankly, I don't care any more - networking was really only going to be a way of sharing a printer and being able to access the 'net from any of our computers. I'd just be happy with a fast internet connection on the desktop - but, today at least, I don't even have that!