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So what i think is happening is the older digital converter box is having issues with the converter in the new TV. Newer boxes will have coax in and HDMI out to avoid this issue.
What model is the new TV? I bet the older TVs don't have a digital converter built in, hence the older box was needed and works fine with those TVs.
You could also try hooking the coax directly to the tv, and do a cable scan on the TV input. Since the new tv should have a digital converter built in.