Hopefully its just the lacquer finish that is bad. My first questions is what is the finish. (gloss, semi or flat ) My second question is.. is it lacquer, or varnish.
You can tell by wiping a small area with some lacquer thinner. if its lacquer, it won't congeal or bubble. There are a few ways to solve this problem.
They do make a brushing lacquer which I have used in these situations. You can also buy lacquer in an spray can. as MEBCWD mentioned above you have to
remove all the dirt and grease before you attempt to prep the wood for finish. I use an automotive wax and grease remover several times to make sure
you get all the impurities off the wood before you attempt so sand it. I like using 1000 grit wet sand paper with a bottle of water and dish soap mix. i also
use lint free paper towels to wipe down the surface. The nice part about lacquer is you can remove it without using stripper. Just wipe it with a rage soaked
in lacquer thinner. You can then mask off the areas around the bad spots and start to apply your finish. I've always applied light coats as needed. I usually
allow 15 minutes between coats. I have also used lemon oil afterwards to keep my casework looking good. It protects against water which is one of lacquers biggest
enemies such as around the sink area. When refinishing, its always best to refinish the whole cabinet frame styles and rails. If the doors are okay id leave them alone.
Just my 02 on the subject. I hope it helps.