The reason that you get a black band across the screen is that you are using a shutter speed that is too short.
The image on the screen is refreshed at a specific rate. This rate differs depending on where you live but it's either 50 or 60 Hz. There are also televison sets that refresh the image at double the rate; 100 or 120 Hz.
The screen is refreshed from the top to the bottom, and when the refresh reaches the bottom, the top has faded to black in time for the next refresh. Thus, some part of the screen is always black at any given moment.
To avoid the black band in the pictures, you need to have a shutter speed that is long enough to capture several frames. On the other hand, any movement in the TV image will of course be blurred if you capture too many frames.
You can try a shutter speed like 1/10 second, which would give you 5-6 frames.