All HD capable means it will accept "air broadcast HD" like your local TV stations and accept them. As for cable, you need cable physical connection unless wifi and is directly supported can do this. You also have to select within the TV the source of any signal so it knows where to go and use it. There, any HD signals or *any lesser signal* is then processed. Any older equipment still needs to be active in that it provides the signal, you just can't grab it or bypass any security in place from protected signal, etc.. It appears you want to grab and not paying for this service now. But, if you're look for local broadcast, then your antenna is the way to go. If your in an area of reduce reception, etc., then you need more than a basic home HD antenna. Like in the old days, a HD ready roof mounted antenna is the way to go and increase reception and "direction" or line of sight of source.
http://www.antennaweb.org/ <---reception needs/antenna
Forget about any cable box converter, yada, yada, that's incorrect info as you're not getting any cable signals because you say there is no cable service in your area. If you can access cable service, then what that service provides for connection is required, check their support website. Same goes for any other signal source, like satellite.
This applies as I stated it. You gave few or little details, it helps to get to a final answer. -----Willy