|The best solution is to buy a router an and Network Interface Card for the desktop. The laptop already has one.|
Network Interface Cards of very cheap and router are not expensive.
The only other alternative is to Install Internet connection sharing on the laptop and connect the laptop and desktop together via cable for which you will still need the Notwork Interface Card for the desktop. However this can be problematic at times and the desktop will be dependant on the laptop. I dont know ho wwell Internet Connection Sharing works on Vista.
The router is by far the best solution. You plug the modem into the router and each computer into the router. The router will come with set-up instructions. That way both computers can be used independently.