I'm not sure I understand the question. The modem connects to the router and both the computers connect to the router either wireless or wired. You didn't post the model of the router, but all routers can support multiple computers. That's usually why you buy a router in the first place.
I'm not sure how you have it hooked up now, but I would think you got a manual with diagrams on how to hook both computers. You may need a wireless card for the desktop if you can't use a cable.