Actually (Orinsear) I did notice another one on the same channel, of comparable strength to where I was using my laptop, so that could have been it. I tried to change the channel, but my laptop then wouldn't see it in its list of networks. Also, I eventually got it (on 2 machines) so it would connect to the router with 'excellent' signal strength and a connection to the internet according to the network map on Vista, but it wouldn't pass data fast enough to load a basic web page.
In the end I guess I took a bit of advice from most of you (thanks!). Nearly all of my internet use is on a wired connection, and I'd rather not disturb that, so I got a Netgear WG602 access point. It took me about 5 minutes to set it up and it seems to talk down the CAT5 to my Speedtouch no problem at all (a speed test with the laptop on wireless about 6 feet from the WAP gave a download speed of just over 6 Mbps for a nominal 8 Mbps connection, which I'd say is pretty good for where I live.
OK, it's about the same cost as a new router, but this way I can put it on the end of a long wire downstairs, where I do all of my wirless laptop surfing, and get very good signal strength there.
So, thanks for your suggestions, which were most helpful. Much appreciated for your time.