It takes a LOT to kill off a SNES, so I wouldn't give up on it until it's been tested thoroughly. If the red light goes on, it probably works.
First of all, I wouldn't ever use coaxial/RF signal to hook up a SNES. First of all, that results in the worst possible image quality you can get, second of all there's a good chance you'll have problems making it work on modern TVs - as long as you're using that, it could be anything.
First, I'd try getting my hands on a regular AV (audio/video) cable for the SNES, those are the ones that look like this:
http://www.tegames.co.uk/media/raw/6FT-SNES-AV-Cable-for-N64-Gamecube-VF401-.jpg
These provide the type of image called "composite", which is still not the best quality, but easiest to test, as they always work! It's the exact same cable used for both SNES, N64 and GameCube, so they should be very easy to come by - if you don't already have one, you can probably borrow one from someone, for testing. These are plugged into one of the TV's AV ports (which I would guess is what you're describing as the "video channels" on your TV itself)
Make sure that your graphic cards driver and DirectX components are up to date.
Some software may interfere on the fullscreen part of a game. Software like teamviewer, displayfusion, or VNC can interfere when a game try to hook fullscreen. Try to shutdown a few running program and see if it works.
Best Answer
That happened to me too. The game was working ok for a few days then a black screen appears after the Activision/Sledgehammer intro. I can hear music but no picture. I did a hard reset on the PS4 and it's seems to work. I hope this helps.