First off, the TV monitor (both ATI and NVidia) say that it is not hot swappable. Turn off your PC and then hook it up to your TV. If there still is not any picture, go to control pannel -> advanced -> displays and try to 'clone' the picture.
The TV and the computer monitor run at different frequencies, so one of the two will lose quality. You must decide which of the two you want to be the main. Which ever one is not set as the primary monitor, will either have the image cut off, very low quality, bad color settings, or no video at all when trying to play a video or a game.
If this still doesnt work, try a different video cable, and if you are using an S Video adapter, try using just an S Video cable.