Alright, well- here's my answer: Yes, you can paint the particle board- just make sure to use a really good primer first. And you'll want to sand the laminate & particle board with a fine sand paper. Use a good oil paint so that it will stand up to high usage & water (from steam, spills, etc.). BTW- I saw a designer on HGTV use Marine paint (like for boats) to paint kitchen cabinets and they sell that @ Mendards, Lowes, etc. [I must add that I haven't used it and therefore can't officially vouch for it; however, I'm intrigued... if it's good enough for Genevieve, it's good enough for me!] And if the cabinet doors are in really bad shape, then removing them and finding an alternative solution is a great idea! I don't love replacing doors w/ fabric [they get dirty easily & are pretty much just a big-ol' pain]; however, I do LOVE pulling off doors, painting the interior of the cabinet and having open cabinetry. Here's a grea example from The Lettered Cottage:
I like that they've used baskets to hide potentially cluttered-looking items [not that I have any clutter... but I've heard rumors that some people do...]. I truly think this is a brilliant solution.
Here's another great example of open storage from The Shabby Creek Cottage:
I like a couple things in this photo: first, take a look at the beadboard used on the back of the cabinets. This is an affordable solution for a very "polished" open cabinet look. Secondly, I really like that everything isn't perfect... yet it looks fresh and clean. This is a great example of realistic open shelving!
Now take a look at this example from Apartment Therapy.
The first two examples were very mono-tone, so I wanted to include this great pop of color! Painting the inside of your open cabinetry a fun or bold color provides interest and instant style! You could also hang an interesting wallpaper on the back of your cabinets... but wallpaper is more costly than paint. And installing it in a cabinet isn't fun [then again, installing wallpaper on a wall isn't all that fun either].
I also wanted to include some paint ideas... I found this example on Pinterest.
If your cabinets are in pretty bad shape, then you might want to do a glazed look. [Much like love, glaze covers over a multitude of sins.] Don't try to hide the distress... embrace it and use it to your advantage [Just say, "Yeaaaa. I want distressed cabinetry... thank you 1960's cabinets!"]! You can go with any variety of colors- just use a glaze that is darker than your base color [the more contrast you have from your base color & glaze, the more distressed look you'll get.]
Here's one more example of a very popular cabinet/glaze color choice from My Sweet Savannah.
Well, I hope this information is helpful! If you have anymore questions don't hesitate to ask, and I'd love to see photos of whatever you choose to do! Good luck :)