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You need to let the laptop into the secret of the new WEP code but before you do that, consider upgrading to WPA or WPA2. WEP is easily hacked these days and you might have fun explaining where the illegal music your neighbours kids downloaded on your account.
If you're using XP, click the wireless icon, go to View Wireless Networks and click on yours. Enter the new key exactly as it is in the router's settings and you're in. Vista and Windows 7 have a Network and Sharing Centre in Control Panel and you click on Manage Wireless Networks then add yours manually.