My hinges are breaking and I don't know where or how to fix

In my experience it’s practically never the hinge itself but almost always the plastic its screwed onto which is much too weak. If it’s only the case which is beginning to crack you may be able to reinforce it by glueing a piece of fibreglass board (eg a piece of an old printed circuit board) to the outside of the case. Use epoxy glue (the sort that comes in 2 parts: resin and hardener).

The hinge will be screwed into brass bushes set into the plastic, and if these bushues are broken it’s harder to fix. If the plastic with the bush in it has come away from the case you might be able to superglue it back in place and when the the superglue has set, build up around it with epoxy glue as reinforcement. But unless it’s a very clean break it will be tricky to glue it back in exactly the right position, without which it won’t be possible to screw the screw into it.