The hinge screws screw into brass bushes set in plastic pillars attached to the base of the laptop case. A common fault is that these pillars break away from the base leaving the hinge largely unsupported. Take care not to strain the other hinge whilst its screws are still in place.

Repair is difficult but a possible method might be to glue the pillars back in place with 2-part rapid epoxy glue with the hinge still attached, before removing the screws. Ensure it's supported and correctly positioned while the glue sets. Only then, remove the screws and build up more epoxy as reinforcement around the base of the pilars.