SNES acting weird

I used to play on my SNES with a composite cable from my brother's N64 and that worked without any problems a few years ago. Since I wanted to play some oldschool games during the holiday, I bought a new composite cable online but to my surprise, I get weird results.

I tried some Dracula and those graphics are good but after the initial intro (with some cool ominous music) the screen turns black and I can't do anything.

Dracula:

I did the whole blowing/cleaning thing but to no avail so I tried Super Mario World but there I have some scrambled graphics. I can still play the game though but with very pixelated graphics

Super Mario World:

My copy of Mario Kart and Dragon Quest V do just nothing. Since I thought it might be a cable issue, I tried the same N64 cable from my brother but that didn't help it. I also tried with an older television set but that gave the same problems.

I do have an RF cable and I tried that on both televisions but then I get simply nothing. I can't remember if the RF ever worked for that matter so it could be that that's normal behaviour but I have played the above games with this setup

I have cleaned the cartridges with a q-tip and some rubbing alcohol and also tried the trick to clean the console cartridge by using a piece of cardboard to the same size as the cartridge contact board. Put alcohol on 1 side of the cardboard and insert it in the slot a few times so it looks really clean.

I'm not really sure if it's a graphics issue since Dracula plays perfectly (except it stops after the intro) but Super Mario World has problems with the graphics and the other two simply do nothing. I can't open the console since I don't have a gamebit screwdriver but is there any way I can determine which may be the error in these games?

Try inserting a shim between the cartridge and the chassis door to make sure that the contacts are touching consistently. Over time i think the contacts lose stiffness and need to be coaxed.