Hi. I'm Steve. I'm sorry to hear about your Apple TV. I will try my best to give you a precise and accurate answer.
Can you give me detailed info about how the ATV is connected to the JVC. Cable type, which input etc.
Ok, I have to mark this as an answer. Please do not click ACCEPT until we are done.
Have you mapped the optical input to the DVD input?
It appears that the coax digital input is already mapped to the DVD input.
Reset the ATV by pressing the Menu and Down buttons on the remote for 10 seconds.
Let me know if that fixes it.