Apparently the modem I'm using (Dynalink RTA1046VW) doesn't like Macs to link to it using WEP wireless security.
It's as simple as that. Who would have thought it would be so picky?
Anyway, on a whim I changed the wireless security to WPA-PSK and now it's all fine. The PC works. The Mac works.
It's like some kind of freakin' CPUtopia. Ebony and (white rounded corners) Ivory.
So that's all fine then. And for anyone who's stumbled across this article while trying to find a solution for the same problem, you're most welcome.