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Thanks again for your time, Vascop, and sorry for the delay in replying - my PC decided to go down with a virus and it's taken me an age and a half to sort it out.
As for DCHP, I've no idea whether I'm using it or not. I know what it means, semantically, but not what it means in reality!
Anyway, I have now got Internet connection through the laptop. Removing the firewall completely didn't solve the problem, so it obviously wasn't that that was getting in the way. So, I did a factory reset - no joy. I then looked for anything else I could twiddle and changed the WEP setting to WPA and, hey presto! It worked.
Thanks again for your help with this - even if advice doesn't work, it's useful to get it as one idea can lead to another in such situations - and all ideas give one hope for an eventual solution!