The boxes are particle board held together with staples.  

The moisture from the dishwasher steam is causing the particle board to beeakndown.

If you want real plywood (over particle board), try Denver Cabinet Express.

It came back negative for asbestos which was a huge relief.This was the kitchen, looking back into the addition.There were several layers of flooring, the last of which was particle board glued to the cement.

But no use printing cheap particle board cabinets since they will still look and feel cheap.

If it is particle board and severly damaged and wont support the new shelf, attach a strip of 1X1 on each side right above the existing shelf and glue and screw to the sides, cut new plywood to slide in on the new rails.

Well, anyhow it cleared the pipes alright and in the process, blew out the p-trap and down went all the food particles that had accumulated in the sink into the bottom of the cabinet, including the liquid de-clogger which ate up the finish on the inside of the cabinet doors. 

The process for converting lead into gold using a particle accelerator is also pretty straight-forward.

But since the core is made of particle board I was sceptical and put a smaple to the test.

For our rental kitchens, we just make sure to get plywood frames (no particle board, as it will be destroyed when it gets wet).