Head over to a dedicated satellite forum and perhaps somone can walk you through the basic of re-routing your coax. There's nothing for less than $100 which would provide the streaming solution you seem to be indirectly asking about. Wired is normally the preferable solution quality wise anyway.

Where does the sat line enter the house? You might see where the initial split is. Maybe it would be easier to find another spot to re-direct the second line from your living room instead of thinking about it as basement back upstairs. Try here too: