The lines on top/bottom of the screen are probably overscan issues. NTSC TV (the old stuff) had massive overscan built into the signal, and broadcasters would allow garbage to show if you actually had a TV that could show it. But most TVs cut off at least 7% of overscan, some more. With HDTVs, many of them have zero overscan and all the garbage comes through onscreen. Or at least zero overscan is an option, you could probably find a setting that would put some overscan back in and get rid of that stuff. Sometimes there is even that mess on HD channels, which should not be. But what can you do, stations are not always very intelligent.
As for the channels that break up, that could be many things. Typically, it wouldn't be the TV, although you could have gotten a lemon, of course. Cable boxes seem to be very hit-or-miss, so I would start there.
You should probably list your settings. No pic at all sounds very strange. Again, I would assume the cable box as most likely culprit.
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