What kind of router are you using?
Are you sure that the Mac WiFi device is compatible with the WiFi router?
The specifications for the router and for the wifi device should say something like:
802.1 G, Wireless G, Wireless A, B, Draft N, N... (Many variants, but, all end in the same result)
Have you tried unplugging the WiFi router for 10 seconds, and plugging it in again? After this, restart the computer (since I dont know how else to reset the IP on the Mac) and reconnect to the network.
Are you sure the router is set up with WiFi?
Can you plug directly into the router and see if it works fine?
Not sure how you release and renew an IP address in Mac... I think on my old Mac, you did it though Internet Explorer... check the Safari settings for network settings, and see if it can either;
A. Detect and repair connection problems
B. Renew IP address