If you think the converter box is bad then get an other converter box ,
http://forum.tvfool.com/showthread.php?t=380.. Also get a different antenna to use as a test antenna , it is a simple antenna , it has no power injector or power supply or amplifier. It is a Real Simple antenna , ANT751. Aim the simple ANT751 antenna at about 136 degree magnetic compass. Here is how to aim antennas ,
http://www.kyes.com/antenna/pointing/pointing.html Do not use the CM3000A antenna or any part of the CM3000A antenna. It's the ANT751 , the converter box , the tv. And yes coax is required to connect the antenna , the convert box and tv together.