I just bought a SNES on eBay and I was pretty disappointed to open the box and see that the port for the power cable is busted (missing the actual port, just had two wires left) anyway, according to other websites I should still be able to make it work. I have the red light shinnjng on the Nintendo console, and have tried putting in different games and resetting, etc. Nothing seems to work. On my tv channel 3 and 4 just show up as black screens with the message "no input". The video and hdmi channels are black too, no sound either. So you think it is because of the port or is the actual Nintendo console dead? I will probably return it but I was super stoked to get this so I thought I better give it a last ditch effort.. I will try to upload some picks of how I have everything set up.
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)