I replied to another thread in this forum yesterday concerning a similar problem. A few weeks back I started having the same problem as you where I was connected to my wireless network but with a self-assigned IP. Note this happened after I updated the system software on my Powermac G4 running 10.5.1, similar to you my powerbook running 10.4 remains unaffected. After trying several things, this is how I fixed the problem:
1. Go into your browser and access your router settings, this can be done in the following manner: http://192.168.1.1
, enter in your admin and password to access. Under the "wireless" tab, click on "basic wireless settings" and change the wireless network mode option to "B-only". If it's already set to that then don't change it. Then click on the "Basic Setup" link, and note the Local IP address, Subnet Mask, and Static DNS1, if there is not Static DNS1 listed, go to the Status link and there should be one listed there.
2. The only way I could then connect to my wireless network, was to manually set all of the parameters. So if you go into System Preferences > Network > Airport, configure IPv4 using "Manual". You can enter in the IP address, Subnet Mask, Router, and DNS server information as noted above.
For example the IP address, choose something like 192.168.1.110; Subnet mask should be something like 255.255.255.0; Router should be 192.168.1.1; and DNS Server should be whatever you noted above.
This should enable you to connect to the internet, your wireless network, and should stop your IP address from being self-assigned. Since you've specified a static IP and even if the router refreshes you'll always get the same address. If you need any further assistance please post and I'll see what I can do but this fixed the problem for me and will not have any affect on the other computers that use your wireless network.