You might try right clicking the network icon and repairing, which should automatically give you new IP address. (It is also possible to be connected to the network without being entirely online, such as when a WEP key is wrong.
You might want to try going to the Network Setup Wizard in the control panel and setting up a new network, it should ask for the network name, type of security, etc.
In the network name space simply put the name of the network you are trying to connect to.
Select the matching security settings. (Most home systems use WEP)
Enter the WEP key. (Usually 9-15 digits)
After the Network Wizard is done, it may automatically connect. If not, try restarting the computer, it should auto connect on login if you select "automatically connect to this network when available" in the dialog box when setting up the Network Wizards settings.