Hey, the slot were the games go into is most likely damaged or needs to be cleaned. If you look in the slot, there is a door that needs to be lifted up and you can see the pins that read the game.
Shine a light into the slot and see if any of the pins are bent out of position or they have a green color corrosion over them.
If you see corrosion, then you can clean it with a nail file. Just be careful, so you do not bend the pins.