I have a TV with a built in QAM digital tuner.
I was going to buy a Home Theater system to go along with it.
For the connection from the Home Theater system I will have an HDMI cable going from it to the TV.
For the digital cable I will just have the cable hooked up directly to the back of the TV.
The question is.....when watching digital tv stations, do I need a digital audio cable going OUT from the TV to the Audio Receiver's input to get it to play the audio, or will the HDMI cable take care of the audio out from TV and into the Audio Receiver?

You'll need an optical cable or coax to to the receiver. Hopefully it will output dolby digital but the TV may just output 2-channel PCM. Check your manual for that or just hook it up and see what happens.