I actually concluded that there was nothing wrong with the hinge, that someone must have knocked over the laptop.
I tried screwing the loose corner piece back in and gorilla gluing it but it didn't hold. I then used a high-strength epoxy and it's holding just fine. Thanks for your help.
If anyone else has this problem, to the hardware store and ask for a high strength epoxy that bonds to metal and hard plastic. Then follow the directions. This should do the trick.