SNES Powers on, works, but glitchy graphics (only certain ones, read inside)

I recently got my old SNES from my old home, where it had been sitting in the garage unplayed for 4 years.
I turned it in and popped in Super Mario World, expecting it not to work at all. It did work, after a few 'resets' and toggling the on off switch.
Super Mario started right up and I began playing. Everything looked normal, it had saved my progress (83 levels) and so I began playing.
First odd thing I noticed was Yoshi's tongue looked odd when he ate enemies. Instead of sticking out, it glitched and went inwards. Ah, that's fine I thought, and kept playing.
Then I got to Yoshi's Island 3, and I noticed that the wooden platform that swings and tips when you put weight on it was glitched and frozen. I tried to jump on it anyways and it disappeared then reappeared somewhere else on the screen, and I just fell through. This glitch is consistent, I can repeat it on different TVs and even after I cleaned the game. I cannot beat the level because of this.
On the ghost castle levels, the ghosts that float in rotating circles were frozen also, glitching in place and never rotating. When I managed to complete the level anyways, I jumped through the finish line and the whole game froze. But on other levels when I finish it ends as normal and I can progress and unlock new levels normally. I didn't understand.
So I popped in Jurassic Park and it worked beautifully, until I decided to go inside a building. If you have played Jurassic Park, you'll know this is where it switches from top down view to first person view, and the graphics kick up. Upon entering a room, I can see the edges of my goggles before the screen glitches, then pixels over and freezes, completely ending the game.
Now, the games play perfectly normally until I get to spots like this, where there are increased graphics or multiple layers involved. I don't understand what is wrong with my SNES console. I am taking it apart this weekend for a good cleaning, but I am worried the problem is beyond fixing.
Any advice/ ideas? The backgrounds play fine, the sprites load fine, and most graphics are perfect. But then some graphics don't work at all, like a layer is missing, making the game unplayable.

 

Check connectors and correct voltages on chips, but it could well be bad video RAM.