New TV

Checking a coax is just like checking any other wire. you will need some type of device to check continuity, I prefer a vol-ohmmeter, but a light bulb and battery will do the job. It is more difficult to work by yourself, as usually you can't be on both ends of the wire at the same time. Try this. Disconnect both ends of the coax from wherever they are connected to. Use the meter on one end to see if there are any shorts in the coax. There should not be any connection between the core wire and the shield at all. If not, go to the other end and connect the core wire to the shield (outside part of connector). then at the first end, your meter should show a completed circuit between the core wire and the shield(outside of connector). If it does, the wire is good. Sounds like the TV is not the problem.