This might sound ridiculous, but I was getting a very similar problem when I first tried hooking up my Super Famicom to the OSSC. Given this was with a SFC, not an SNES… I imagine they behave similarly. I hadn’t used my console for quite some time, and since it takes the OSSC a while to sync, I wasn’t seeing the flicker from the power turning on and off, and I was just getting a black screen on the monitor. It was picking up the signal from the OSSC – just a black screen. I decided to pull out my Composite cables to make sure it wasn’t a problem with my SFC, and I was noticing the flicker from the power turning on and off… So I then thought that maybe my game just wasn’t seated properly, despite having just cleaned the connections. Sure enough, my console was just struggling getting a clean connection with the game pins, and after jiggling the cart and turning the console on and off a few times, the picture came back. Plugged it right into the OSSC after that with the Insurrection SCART cables, and bingo – it was working just fine.
This might be a long-shot, but is there any way you can verify that the game is seated properly? Most HDTVs still have composite inputs – that’s what I ended up using, and they are the most common connection that come with consoles. If not, try taking a game that doesn’t have any valuable save data on it, wiggling it around the connectors, and turning the power on and off a number of times. Wait a few seconds every time you turn the console off and on. There’s a chance that the SNES just isn’t getting a clean connection with the game. I mean, it’s worth a shot, unless you know for sure that isn’t the issue. Good luck!