You don't say much about your settings there, so will be hard to help you. But check DHCP settings on both the router and the adapter. Check the DHCP service is activated on the router, and that the adapter has got "automatically obtain IP address" (or something like this, my Windows has never been in English, so i translate from litteral French ) checked in its properties box.
Also check whether you have WEP enabled or not, because you need to give every adapter the good WEP key (the one that's set on the router) to allow them to connect to it. If you are in a single house and don't fear to share your WiFi with neighbours, you can simple deactivate WEP on the router, will be much simpler if you aren't an expert in networks.

HTH, but can't find your exact prob as you say very few about it