It will work, we just need to clear the air on a couple of points.
If you have an existing dial up connection configured on the laptop you should delete it for the time being.
Now make sure that the Desktop broadband connection is configured so that the laptop can demand a connection if one doesn't exist. You do this by right clicking on the connection and selecting properties. Click on the advanced tab and put a tick in the box that says 'allow other network users etc............'
Then make sure there's no tick in the box that says 'allow other network users to control or disable etc...........'
Restart the desktop and establish a connection. Now start the laptop, and you should see Windows pick up the internet connection. Watch for the familiar small monitor icons - there'll be one for the wireless network and another for the broadband connection. Launch Internet Explorer and you should see the homepage load.