Two weeks ago I moved again and it took until yesterday that I got internet access again, now using cable. This actually rocks, it is really fast, 6 Mbit/s. I still can remember, I think it was in 2001 I still had an analog modem with 100something kbit/s. That's really an incredible increase in speed in just 6 years !
I also got some more experience with WLAN under Linux, especially under Slackware 12. kwifimanager somehow didn't completely do what I wanted (and I didn't feel like reading a lot of docs), and knetworkmanager doesn't come with Slackware.
So I just had a look at /etc/rc.d/rc.inet1.config, and voila, everything there. This file contains prepared sections for several different network interfaces, including WLAN. So I entered my settings in that file, executed /etc/rc.d/rc.inet1 and was online again :-)