From the information in your post we would make these initial assumptions.
1. Your lap top ngets to the Internet through a wireless connection and you have a wireless router that works either on cable or DSL.
2. Your desktop computer has not been on the Internet and you are just now trying to get your desktop computer to access the Internet by direct connection to the router.
If the above correctly represents your situation, Here is what you would have to do. You would have to run the network wizard under Windows XP and set up a local area network for your computer using the router as the network source. Once properly set up, you should get to the Internet and also see your laptop in the network places.
You did not mention what type of laptop you have, what kind of router use, or what sort of Internet connection you have. These details could make a big difference in the answers we would give you. And what kind of Desktop.
Details matter.