What I can see from your post, is that you would like to know how to connect the Slingbox to the Audio and Video Source.
In this case, you can connect the Slingbox to the coaxial cable coming from the wall, and then from the Slingbox output to the main TV if you want to make a pass through.
That is one option, however, if you have the coaxial cable coming from the wall into a Cable Box for example, then you can make the connection from the Cable Box to the Slingbox using RCA cables, S-Video or Component.
You can check the following links with some troubleshooting steps and information about the connections that you can use with the Slingbox. Also, please be aware that the Slingbox is not compatible with the HDMI at this point which might be the main reason why you can't get it to display any audio.
Since it sounds like the broadcast stations that your TV is receiving are coming from a cable box, then I believe that you want to first disconnect the cable that connects your cable box to the TV. As Josebrennes notes, the Slingbox may not work correctly if this cable is an HDMI cable. Instead, you should connect the cable box to the Slingbox with a five-wire (red-blue-green for video; red-white for audio) component cable set; then use a second set of these five-wire component cables to connect the Slingbox to the TV. Doing so will allow the HD broadcast signal from your cable box to be "passed through" the Slingbox to the TV, as well as to allow the Slingbox to send this HD broadcast signal through the Internet to wherever in Internet-Land that you want to view what the cable box is sending to the TV for its broadcast signal. Note, however, that to get a quality HD video signal sent out from your Slingbox to the Internet, you will need to have reasonably fast UPLOAD speeds on the Internet Service that you have at the physical location of your Slingbox. For HD signals, this upload speed must be about 4 megabits per second, or faster. If you would be satisfied watching standard definition programs only from your Slingbox, then upload speeds of about 1 megabit per second would be sufficient.
Write back to this forum if you continue to have setup problems, and folks on this forum will certainly help you out.