Disabling DHCP on the Speedtouch and enabling DHCP on the Linksys - didn't work.
OK - try again from first principles. Wiped everything, and rebuilt the configuration of the Linksys, wired, with the Speedtouch disconnected. When it came time to change the IP address of the Linksys, I lost comms. Turned off the Linksys, turned off the PC, connected the Speedtouch, turned on the Linksys, turned on the PC - and voila - all working.
So the Speedtouch is the router, the Linksys is just a dumb ol' WAP.
Do you know what caused all this problem? I tried to change from WEP to WPA
without checking that my wireless card in my notebook could support WPA...
Thank you all for scratching your heads on this one!