The best way for several Reasons is a new TV, the newer flat panel TV's use far less power, many of them can run off 12V, same as your concertone.. You may be able to fit a wide-screen in the hole (slightly shorter) for HDTV, and of course they are already digital.
Opton is the converter.
So, what do do with the existing?
If it's small enough use it as your "Sat findr" when you are pointing your DirecTV antenna (or dish)
Simply feed the sat receiver to the outside TV jack, take a "Jump start" battery and the concertone to the antenna site and, after you make all connections, go in and set the receiver to "Antenna pointing" (On dish that's menu 6-1-1 as I recall, not sure how to get there on DirecTV)
Now watch the screen as you aim the dish.