[Arran]

I have found that acrylic solvent cement works very well for gluing polystyrene cabinets, it basically welds the plastic back together. As for teh broken studs you can also glue new plastic studs in place of the old, again with the same cement. Or better yet, glue machine screws to the front with epoxy, head first, then you can use nuts and washers to re-attach the front, then it can be removed again should it need to be cleaned or re-restored.
Regards
Arran