Cut the cable, what now for the coax?

[Angrboda]

We have a TV, blu-ray, a laptop and a PC in the office. The router is hooked into the modem and everything is LAN'd off the router. I'll see what kind of coax options those two have right now, but I would still need something like the Actiontec at the other end, I think. I don't know if the coax connection on the TV would share connectivity with the Firestick.

Connecting the coax to the TV will not get internet to the Fire Stick. The only way to do that using the coax is to put another adapter, going the other direction, on the end of the coax, and hook the ethernet out of that adapter to the Fire stick. (If I remember right, there are options for hooking ethernet cable to a Fire stick, but I may be wrong and thinking of the Chromecast or Roku instead.)