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You might be able to find reused cabinets that fit from the Restore or classifieds. the cheapest way to do them new would be in-stock cabinets and doors from a big box store like Home Depot or IKEA. :)
You can sand the particle board once it is dry until it is smooth with the areas that didn't get wet. Then they can be refinished. This way, you don't have to replace anything.
You may be able to find new doors and drawer fronts that fit and you could replace them. Menards, Home Depot, Lowes, etc stock cabinet doors and drawer fronts and you can order them online as well. If you have any DIY skills and the proper tools you could make some simple cabinet doors and drawers from new materials.
https://housefulofhandmade.com/how-to-build-cabinet-doors-cheap
https://fixthisbuildthat.com/how-to-make-drawers-for-a-cabinet
Measure the doors and check with your local home improvement store. If they are standard size you can usually get replacements there for not too much. Also, check places like the Habitat for Humanity home stores.
You can purchase doors or you could use plywood and 1x2 or 1x4 to make your own doors in the shaker style. If you are interested, I think there's a project showing how to convert plain to shaker style cabinets.
here is an idea for your project
https://www.diynetwork.com/how-to/rooms-and-spaces/kitchen/cabinets-should-you-replace-or-reface