With the current connectivity of todays TVs, the use of Home Sound Systems, and satellite receivers, the best thing is to scrap that distribution switch box unless it is the power source for the batwing antenna. If it is, then leave the antenna connected but disconnect the rest of the cables.
The satellite to TV connection should be anything but coax. If you have a DVD player, connect it direct to the TV again with anything but coax. Still using a VCR? Well that is an issue onto itself.
That distribution switch box was a good ideal in the days of coax antenna connections for everythings. It days are past and coax (outside of coax to the satellite receiver) should be only for the batwing antenna.