If you can't close the door, it does not function so well either. Unplug the cooler, let it warm up completely to room temperature, maybe even add a little heat, but not too hot, warm to the touch, from a hair dryer, and give it a shove back in with the part of your hand that is near the wrist. You may need to pull it out of the space, lean it back a bit, but not too much, the refrigerant doesn't like it. and push it back in.
There was something that did that, it must have somehow been pushed severely from the back side, at least so I guess. Check the back for any sign of abuse that may keep it from going back in.
Before you try that, the crease is really predominate at the corner. After warming it up, put JUST your thumb over the middle of the sharpest part of the crease, and push steady and hard if you need to, the rest should follow. If you have a well rounded LARGE handle you may be able to use that instead. Since the handle has no feeling you will not be able to govern how the progress is going. It may be more prone to cracking the PVC shell that is deformed. If it does, humidity may enter the casing, that may or may not be ok.