Are you sure you can connect a "broadband TV set box" to a router? I've never heard of connecting a TV to a router, so I was just wondering whether you know, for a fact, that can be done. Is the "broadband TV set box" a device designed specifically for connection to a computer router, which I presume is connected to a cable modem?
Do you not have TV cable wiring to any other room? What about using a cable splitter and running a standard coaxial cable to the TV?