As it seems, there are dozens of other users who experienced a connection timeout using AirPort W-LAN connections on Macs. There are dozens of different solutions described in the forums, I tried plenty of them. From reboot to deleting the WPA2 key from the keyring, nothing worked.
Eventually I tried the following and this worked for me. (Note that I’m using a German installation, the real English translation may be slightly different.)

1. Go to Mac (the Apple symbol in the top left) -> Location -> Network Settings
2. Click on the “Airport” entry on the left
3. Click on the “additional options” button
4. On the Airport tab, click the “+” button below the “preferred networks” list
5. Click on the “show networks” button and select your W-LAN from the list
6. Enter your password

That way, I could connect without problems. It may be coincidence that exactly this way worked, and none else, but maybe there’s really some strange difference.
Let me know if this helps.