Ultralayman mode - ENGAGE!
Cables are easy. Yes, the grey ribbon cables connecting the boards. I give 'em a good blow with compressed air and visually confirm pin health.
The socketed EPROM's and PROM's are the actual game data storage chips on the pcb's. They "plug" into their little black holsters. They are labeled with stickers that say things like "TKG4-C 5Af." The "5A" refers to it's home position on the pcb, row 5, position A. And the "C" means it goes on the CPU side of the board (labeled as such in white text next to the Nintendo copyright).
You need to carefully pry up and remove the 4 chips I stated on the video pcb with a electronics screwdriver or chip puller. If you apply too much pressure or lift to one end of the chip, the metal legs will break and the chip is useless, so be sure to pry evenly on both sides, back and forth until removed. Do them one at a time so that you may visually confirm their proper orientation, as reinstalling backwards will also render the chip useless. Then use a pencil eraser (red are firmer) to carefully "sand" the outer surfaces of each metal IC (chip) leg until they are shiny (they're probably lightly coated in black gunk or white residue). They are small and bendy, so be careful. I brace the leg backs with my index finger lengthwise. You can bend them back and forth a bit before they snap, and you will need to bend at least one side of each chip's legs inward slightly to reinstall them, as they will splay out when removed.