...which TV make/model do you currently have?
FWIW, I connected a media streamer (WD TV Live) to work with my dad's older Sony Trinitron units. He also has one of those rural '50 cable channels for 50 bucks' providers. No DVRs are available and it's coax only to the TV. But at least he didn't have to chop down thirty nice 80' tall trees just to get a satellite signal (LOL).
FWIW, the Sony box doesn't have a tuner built in, so that's where you may have issues. See, the cable box or sat box would be doing the tuning (=modulating), so the HDMI input on the GS8 would be able to accept such a signal. If your (HD?)TV is doing the tuning, then that's where the box wouldn't be used as such- only for sending along internet content to your (HD)TV.
Hope that helps a little more.