I agree with the author about most paint/primers ability to prime, especially in your case with hardwood cabinets… however some applications will work, such as exterior unprimed wood… now in your case I would lightly sand your surfaces and then apply a coat of Pigmented Shellac Sealer Primer (avail at any paint store), this should SEAL IN the paint that is there… then finish coat with regular high grade interior semi gloss paint… Good Luck!