To fix the doors would require somehow getting glue back between all of the layers of veneer consistently, and then clamping them flat and letting them dry. Then, after un-clamping them, you will throw them away, because they will look really bad. The hardware is salvagable. The knobs in your picture are glued into a drilled hole. Just give them a really good wiggle and you will break the glue joint. then they pull right out.
Some people are really into keeping the original hardware and some are not. Purely a personal choice. I would replace all of the doors at the very least. the knobs are not hard to re-use, it just takes the same thickness of door to have them latch securely. That should be easy to acheive. The hinges are probably re-useable as well.
Are the interiors of the cabinets in as bad shape as the outside? I would be suprised if they are. Like I said before, it may be possible to replace the exterior parts of your cabinets, while saving all the interiors and face frames. If you need more precise information on how to go about doing this I would be glad to help. Woodworking is in my blood.
Good luck, Rich