Looks like the roller that the hinge rides on has broken and is now off center. Has anyone ever fixed something like this? What would I need to do and what part would I ask for?
93 Lesabre
http://amopower.com/files/Buick/DSC00866.JPG

That's the detent roller and pin. It is part of the inboard hinge half, but some places offer a repair kit including the roller and pin.