Which OSSC (Hardware and Firmware) Revision do you have?
I have Audio out on mine through the cinch even when turned off.
Next, when you connect it, what does it display on the OSSCs display?
Does it get sync (Green LED only?)
For the SNES you’d want something along “AV1: TGBS 262p 15.59kHz 59.53Hz” on the display.
Do you have HDMI selected in the output options -> Menu -> Output Options -> TX mode -> HDMI ?
Finally, one of the ICs on the board might be fried.