Painting Pressboard Cabinets

Hi, Our rental apt bathroom cabinet was made of that stuff too. It was pressboard, but had plastic over it that was falling off. I peeled off the loose plastic completely to expose the pressboard. It had a decorative plastic edge that stayed on so I left that there and I lightly sanded the cabinet and plastic parts. Then I used 2 coats of primer on them, and painted it white. I used Kils primer and white latex paint and that's it. That was 2 years ago and it still looks great.
Just make sure you prime all the exposed areas of the pressboard so water doesn't get on the wood.

I'm not sure this will hold up for very long, given the cabinets you're starting with. Is there a way to add a wood veneer on top of the cabinets? More work, but it would last longer.

I agree with lorraina, but I think they should be sanded first to help the primer adhere better.

I would use an oil based primer for the first coat and then an oil based paint for the coat of your color.