Jackie is right. Remember to temporarily disable your wireless network connection on your computer first though, to make sure you are using the ethernet connection (wire) while you are jury rigging (cloning the MAC address of your computer onto the wireless router) the router.
And yes this is because the cable ISPs would like to charge you extra for more than one computer connected to the Internet, since they already have some customers paying extra. But in today's world of so many network connected devices, that is not realistic. So your router disguises itself as your computer. (Somehow on the Cable ISP end it would seem they are able to tell the difference between a computer's and a router's MAC address perhaps.)
And then the router shares the internet connection. You could leave one computer running and share it's connection as well, but that would be a waste of a computer and probably more power use also, which would accomplish the same thing (using a computer as a router,) with the wireless router connected to that computer, which would complicate the setup though.