As Jon said the hinge is held in place in my Boler
is with rivets. If I had to do it, I would get a thin strip of metal and drill two holes in it to match the hinge. I would then then put the rivet through the hinge, through the fiberglass, and then into this piece of metal to give it more support inside of cabinet.
Riveting is very easy with just the pop rivet gun and rivets to buy.
Place pin into the gun, put rivet into the holes and squeeze the handle till it pops the pin off. Simple.