It depends if you have setup your wireless or not. If you do start run then cmd press return and type ipconfig /all you should get a list of your network and the wireless network. both should have a simliar setting all that should be differant is the ip.
It depends what you are using for wireless if its a firms software that came with the card then it should give you an option to connect. If not you can use the windows connection.
Have you setup the router to be a dhcp server(I assume so if th e other laptop is working)? You can get the setting from the ipconfig /all command and manually give the wireless an ip a few numbers up so its got the right settings(the problem with this is if you go to another network it wont work). But giving a fixed IP would prove it works