The post says he has a router "linksys wireless-g access point router" ???
If it is only an Access Point then Joed is correct you need the router to access your broadband with more then 1 PC
If you have a wireless access router then here are the instructions:-
Easy Solution (you should be so lucky)
Sometimes the value for the Wireless Key is written on the underneath of the router, look for SSID (this is the network name) and WEP or WPA key (called the encryption key) Alternative Method
In order to find out your Wireless Network Key you must first use a cable to connect to your router.
Once connected check that you are connected to the internet by opening Internet Explorer
The address or the router is usually one of the following values:- http://192.168.0.1 http://192.168.1.1 http://10.10.0.2 http://192.168.2.1 http://192.168.2.254
Try clicking on each and see if you get a logon box popping up
If you do, that is the correct address for your Wireless router, note it down.
If the box has the username and password completed, then click OK
If there is no value for username try "admin" and for the password try one of the following "password", "admin",
Also try nothing for the username and "admin" for the password
Sometimes the value for these are written on the underneath of the router
Once the router page is displayed, look for an item called Wireless Settings.
Next see if a further option for Wireless Security exists.
The names of these items vary from Router to Router
Once security is displayed the SSID (Network Names) and the WPA or WEP Key can be found.
If there is no security I would set it to WPA or WEP then the original computer connecting will need this value if it is connecting wirelessly