Just to clear up a few things. The router should be set up properly if one PC can use it to get to the www. Lets's forget all about wireless for now, and assume everything is wired. Once all the below is checked, substitute the word network for wifi! ;-)
Provided the network card in the laptop is not disabled and ip settings are set up right for it you should just be able to connect to the router and access the www without doing anything else.
To set the ip settings, open Network Connections in Control Panel. Right click on the Local Area Network icon (or wireless one to use wifi - setting one will not set the other) and select Properties.
Click on Internet Protocal (TCP/IP) and click the Properties button.
Click the radio button Use This IP address and enter the following:
IP address: 192.168.0.100 (This is your laptop address on your LAN, must be unique)
Subnet mask: 255.255.255.0 (Automaticly entered setting)
Default gateway: 192.168.0.1 (This is your routers IP address on your LAN)
These are not specific IP addresses, but they are kind of most common, so in most cases if defaults are used, they should work.
Just do the same for wireless network card, and it should work.
DJ OD