Yesterday I bought a Linksys 54-g card for the laptop. The installation is very simple: just do a setup with the supplied CD, reboot and insert the card. Windows then recognizes the card and uses it. But when I switch to using WEP (since the AP is), it would not connect to the AP. After much trying and changing settings, I found that you just have to wait a little longer than I expected. A proper reboot after changing the settings and then waiting until the connection is made did the trick. After that first wait-till-I-get-my-settings-confirmed-with-the-AP, things are smooth. Reboot until network-up-and-running is faster than with the 3Com card. And the link quality is a lot better: signal strength and link-quality in the 90%-range.
Great, now we can surf the internet downstairs again, without bugging the connection to the computerroom upstairs.