There should be two pins. one on each side and 2 screws that go into the pins to keep the sides from accidentally coming off. You place the side hole over the pin and then press slightly from the other side to make it go over that pin. Then screw the screws into the end of the pin.
Looking at your 1st picture of the inside, i bought all new lid hinges, that came with screws to fasten the hinges to the cooler. On all hinges but one, I was able to use the screws to fasten. On the final hinge, there was nothing to thread the screws into. Do I need a rivnut in the hole on the cooler top, to be able to thread in the screw?