KYGMSY - the Win98-equipped laptop works perfectly. I'm not going to fix what isn't broke!
SSC - I have a perfectly serviceable wireless router in the WRT54G. My [second] question was 'Who makes an ethernet ADSL modem that I can connect directly to the router - or is there a solution with my current kit?'. But thanks for the link!
ORAC - Iwas pretty sure that shared internet access would not be possible with my current setup, but you never know when someone might have a clever workaround! I think the sensible answer to that problem is a Linksys BEFCMU10 Etherfast ethernet/USB modem. I'll try disabling the authentications and see what happens with the network; I had suspected that the solution may be in that direction - unfortunately my firmware is fully up to date, so no help there!
Thanks all.