I would take good photos to the home improvement store and ask them for ideas and advice. They will be able to give you hints on preserving the cabinets as well as how to fix them cosmetically. They have the latest materials and application tools to do the best job.
If it's at the floor you may be able to glue(it reinforces the wood) then nail a wider base board.
You really can't fix the damaged particle board, all you can do is reinforce and cover it up.