any chance you can take a picture of the screw?
Once a plug is broken inside you're better off to buy a new one and put it on instead of trying to rig and old broken one to work. If you manage to get inside the old one and fix that it's just a matter of time until you're having to open it up again to fix it again. When it comes to electricity and water its just a much better idea to replace it and not risk the GFCI failing and killing whoever is using the machine.
Once a plug is broken inside you're better off to buy a new one and put it on instead of trying to rig and old broken one to work. If you manage to get inside the old one and fix that it's just a matter of time until you're having to open it up again to fix it again. When it comes to electricity and water its just a much better idea to replace it and not risk the GFCI failing and killing whoever is using the machine.