Briefly, I've installed the drivers etc. for the Cisco card on the Jornada and it's working. No doubt about that, since I can access the router and network hard disk setup menus by entering the correct IP addresses. HOWEVER, I can't access anything by other means, e.g. when I enter http://hermione for the network drive, instead of the IP address, it can't find it. This also applies to URLs for sites which are working when I try them from other computers.
Presumably something is wrong in the way URLs are being handled, I just have no idea what.
Later If I ping sites from another computer and enter the IP address into the Jornada it can access them, so it's definitely working and connecting to the internet. Trouble is that every link is another address, so this is not much use for practical browsing.