This cooler is probably nearly 30 years old but since it still works so well, I decided to create a replacement hinge for it. I'm sharing it here in case someone happens to have the same cooler, and the same problem. 

It appears that this is a weak spot of these coolers and more people have the same issue with it. There is even another fix for it here: https://www.printables.com/model/295568-hinge-for-old-camping-fridge I didn't want to drill holes in the side and I can't currently print PETG, I decided to make something close to the original shape, that is hopefully sturdy enough to last a while, even in PLA. Like the original piece, this model allows you to adjust the lid up and down a bit.

BOM

• 4x 4x32mm panhead screws
• 4x 4mm knurled threaded insert
• 2 component epoxy glue kit (make sure it's safe for use with polystyrene).
• Couple of grams of PLA.

Disclaimer, before you follow these instructions and fix your cooler, please note the following for your own safety: 

These coolers are made of polystyrene, also used to make styrofoam. Polystyrene will release styrene when heated and/or coming into contact with solvents. When you follow the steps below, please make sure you are in a very well ventilated room, I did it outdoors. Styrene is very dangerous carcinogenic substance, it can cause skin irritation, sore eyes and throat, and breathing problems, even in small quantities. In particular make sure you use a glue or epoxy that is safe for use with polystyrene as it can both ruin the panel and your health if you don't.

Instructions

• Print the left and right piece standing upright, no supports needed, high infill (e.g. 60%, gyroid). 
• Remove the pins that holds the lid from either side and keep them.
• Cut the leftovers of the hinge parts clean off with an oscillating multitool, jigsaw or Dremel. Doesn't need to be perfect, should be smooth. See pictures.
• To attach the pieces, drill 5mm holes in the places the (4mm) screws land. 
• Heat some knurled threaded inserts and insert them into the original panel. Do this outdoors or make sure you have plenty of ventilation. You can use a soldering iron for this, alternatively screw the nuts onto a 4mm screw, hold the screw with a pair of pliers and heat the nut with a lighter. There are also commercial options available. 
• Next up is the epoxy but first make sure you apply a scrap piece of paper or plastic to close off the holes of the nuts on the inside of the panel, so they don't end up filled up with epoxy. 
• In order for the nuts to stay in place better, apply a generous quantity of epoxy inside the panel until the nuts are entirely encased in it. Make sure to use an epoxy that is safe for use with polystyrene. Do this outdoors or make sure you have plenty of ventilation. Do only one side at a time and place the panel such that gravity works in your favour. 
• Wait until everything is dry.
• Take 2 4x32mm panhead screws and screw the pieces onto the panel.
• Put the pins into the new hinges and put the lid between them.