Milo - thank you again.
A quick update ... spent an hour plus attempting to connect wirelessly on the Dell with two different adaptors - no joy. Reconfigured the router to WPA PSK security and the Nexus couldn't connect either!! A further reconfig to WEP and the Nexus is back in business - I read your last while on that connection.
I much appreciate your efforts to make useful sense of this problem but given that my primary concern, at the moment, is to make sure that SWMBO can use her new toy for browsing, I think I shall 'quit while I'm ahead'!
There are, obviously, issues with the laptops and, given that I can hook them up on ethernet cable, if needed, I'll give my rapidly reducing brain cells a rest!
Again, thank you.