Two things to try. (If you have dial-up I do not know if these will work.) Shut down your desktop and then hook up your laptop INSTEAD of your desktop. OR Get a wireless router and both can be on the internet. Routers from NewEgg.com are available under $30 - some under $20. You will want a wireless N router. I like Linksys but they are $40+. To check out this method, you may be able to borrow a router from a friend to test your system. And you may have to buy an additional Ethernet cable if the router doesn't come with one.
I don't believe there is such a thing. if you're looking for wireless internet on a desktop you can hook an internet enabled smartphone such as one of the droid series to get internet. It costs you though. Another way would be to buy a wireless adapter card and install it into your desktop. They're very common but they cost a little over $50.00 for a good one.