While you can sand and paint particleboard cabinetry, I can't guarantee a wonderful or durable finish. This fix can make them a good deal more presentable. Sand the cabinets first and get them as smooth as you can. Then I would recommend an oil based primer. Latex primers will raise the particles in the board creating a rougher look. You way have to sand again with fine sandpaper and apply a second coat of oil based primer. The topcoat with two coats of 100% acrylic paint. Try to find a finish that will "level out" and give you a nice finish look. I have had good luck with ProClassic from Sherwin Williams and Cover Stain primer from Zinnser.