Fixing scrambled graphics on SNES console

Whenever I try playing a game on my old SNES console, the graphics come out either scrambled or completely black, but the audio plays correctly, and the controls seem to work just fine. I initially thought the problem was a dirty connector on the game cartridge, but even though cleaning it did remove some dirt, it didn't improve the graphics at all. I have the same problem with each of my game cartridges, although some cartridges come out with worse graphics than the others. I double-checked the connection to the TV, and tried both the RCA connectors and the RF switch, but I have the same problem with each. It seems as though the problem is with the console itself.

My SNES was in perfect working order as little as two years ago. What else can I try to do to fix the problem and return my SNES to a usable state?

Most likely one of your RAM chips has gone bad. You may want to evaluate purchasing a used console vs. what your time is worth fixing the old one.