The audio for your cable service originates from your cable box and passes through your TV to your audio system. You state it's a composite connection from the box to the TV, meaning you likely have a yellow video cable and red/white audio cables.
You can still use an HDMI cable even if you aren't paying for HD service. The box will still pass standard definition video over the HDMI. My guess is that there is a problem with the box, since all other devices connected through the TV have proper volume, or the RCA input to your TV is malfunctioning. You will either need to switch to the HDMI output or possibly have your set top box swapped.