HDMI output from cable box feeds the HDMI-1 input on the back of the TV. On the TV, the two RCA audio outputs (colored red and white - use the ones named "Audio Output") on the top right will feed one of your audio inputs (you should be able to use Video-1 or 2) on the HTS.
Make sure you set each device to their proper input. If you can't get video through HDMI, try the component video connection from your cable box to your TV. You'll need a 3x RCA cable to hook each one up; happily, they are usually color-coded RED, GREEN, and BLUE. If you can't get audio, try switching the output from the TV to another input on the HTS.
For more info on your TV's connections, check the manual:
https://www.mitsubishi-tv.com/asset/file/owners_guide/WD-52628.pdf
The Sony manual is at https://docs.sony.com/release/htddw750.pdf.