[Arran]

I would just use a wood glue, and some sort of clamps, binder clips will probably suffice, to put the large pieces back. To me it looks like there enough pieces there to perform a near invisible repair, at least with the walnut veneer that goes on top, save gluing the walnut veneer on for last. If there are small chips out of whatever is underneath some filler should do the job, you can shave off the excess with something like a scalpel or x-acto knife, and sandpaper. The part you show with the dent, that can be fixed with carful use of a damp rag, or paper towel, and a clothes iron, a soldering iron will also work, placed right over the dented area. When your cabinet had a finish on it, a lot of the damaged areas would have been covered by paint or shaded lacquer, so al long as the pieces are glued in straight, and smooth, they will be nearly invisible once a finish goes back on.
Regards
Arran