Ok, I took time today to look at that.

I installed Airport Software 2.0.4 (I had 1.2 installed, that came with OS 9.2.2). Now it kinda works better: I can connect to my network using the wep password. But that's about it: no local nor internet connection. TCP/IP control panel gives me a random local address (169.x.x.x), but my network is of the king 192.168.x.x. It does work fine under OS X, and under OS 9 using an ethernet cable, though.

Any further idea?

EDIT: sorry, I forgot to thank you all for your time and suggestions!