I am a bit confused, but will clarify what I think you are saying.
You have a TV Tuner card in your box. When you fire up an application that shows TV, you don't get audio. But, in those applications (let's use xawtv for example) if you switch the input from Television to anything else you lose that video, but it allows your audio to work.
It sounds as if your audio input device (recording) is not setup correctly. I am further assuming that you have the audio out on your TV Tuner card plugged into the Line In on your soundcard. If so, then:
Open up your audio mixer by opening up a terminal and typing:
alsamixer (this is in the alsa-utils package)
Once that comes up, press:
Then to select the Line-In option as the recording option, arrow over to it and press SPACE.
Post back and let us know how things go.