Note: I have almost no hair! OK, my new laptop seems to work fine and I have been able to get online with it whilst the LAN cable is connected. However, so far I have had no success getting it to connect wirelessly. I thought earlier on that I had corrupted the profile in the router itself so I wouldn't even be able to connect wirelessly with my older laptop - luckily I was able to sort that out with a factory-reset of the router and reconfiguration.
I think my next port of call will be my ISP, through whom I purchased the router, to see if there are any compatability problems because my new laptop uses Vista rather than XP; the router manufacturer's website seems to indicate that there may be, but as it is written in a kind of tech-speak jargon I am not entirely sure.
Off for a long walk on the beach!