What do you do when you discover a cabinet shelf is sagging? Well to start, it's probably a good idea to remove some or all of the weight off of it. The chances are good that it started sagging due to poor quality of the shelf material, and maybe that the shelf got wet and the weight on it started the sagging process. We see this a lot underneath kitchen sinks...a leak will develop and won't be discovered until it's too late. By that time, the water has saturated the shelf, and the weight of detergent, trash can, water filtration tanks, etc. will cause the sagging.
You can always build a stronger shelf out of ¾" plywood and put a solid edge on it. The edge acts as a brace to stiffen up the shelf. The edge can be made of 1"x2" solid wood and can be painted or stained to match the existing shelves.
When replacing the base of a kitchen cabinet, you really have to plan on the cabinet base getting wet. At some point, there will be a leak and the floorboard will likely be exposed to water for a period of time.
Melamine is a good product to use. It is basically particle board covered by a water-resistant plastic. If water leaks into the cabinet, the wood won't be exposed to the water and won't become damaged. The challenge is that the size of the cabinet floor is fairly large. You can't get a replacement board in there without either cutting it in half or by removing the cabinet support, installing the replacement floor, and then reinstalling the support.
Sometimes the support is held in place with a plastic bracket which can be removed. The other option is to cut the support with a hand saw, install the board, and resecure the support.
Cabinet drawers can also suffer from abuse. Here is some information on cabinet drawer repair.