Prime Instant Video is simply a streaming service from amazon. first you need to subscribe, then you need to have an internet connection in your house. if your TV is a smart one, then you simply plug your internet cable in the TV. if your TV is not smart, then you need to have a computer connected to the internet, down-stream the video to your computer ans then push the signal to your TV with an HDMI cable. if all this is not clear to you, then simply go to the movies!
First off, do you have an audio receiver with HDMI out to a TV? If so, use it. Otherwise, use an open hdmi slot on your tv to connect your xbox . This connection should work. I recommend going to setup>first time setup and and go through the steps again and label your xbox hdmi (say... 3, if you are using the others) as 'GAME'. I'm not sure if it is set to automatically adjust the resolution/HDMI connection settings or not, but I have a hunch that is the problem. If it still doesn't work, go into Picture>HDMI settings and make sure the port used is set to Auto. Also under 'Content type' set the port to auto. If this still doesn't work, someone else with more hands on experience will need to help. Also, it never hurts to upgrade your tv's firmware, although it should not be necessary.