Your son's TV uses a breakout cable (also known as a dongle). The pinouts (the location and purpose of each pin) for breakout cables are not standard. What works for his TV may not work for your satellite receiver.
Your satellite receiver has a 10-pin mini-DIN connector. It is definitely not an S-Video connection. S-Video uses a mini-DIN connector with 4 pins, It always has 4 pins, and the pinout is controlled by a standard so it is always the same.
A 10-pin mini-DIN connector may be for a breakout cable that includes S-Video and stereo audio, but it could be for other video connections such as component video, stereo audio, and composite video.
Maybe if you tell us the make (Dish, DirecTV, etc.) and the model number for your satellite receiver, we can help you find the right part for the job. Otherwise we are just guessing.