Yikes! Just keep going up the chain of solvent-based cleaners until you find one that will dissolve what is on your cabinets . Hopefully you can do this without hurting the finish, but if that is what is stained, you may have to remove this and re-apply. I would try these cleaners first with a paper towel, then with a scrubbing pad (like you use of non-stick pots) then with very fine steel wool. I would try in order: denatured alcohol, ammonia based cleaner ( Fantastik), ammonia (straight), mineral spirits, lacquer thinner. Warning: Stay away from NAPTHA or MEK other solvents that would work but are far too nasty to even have in your kitchen! Once you get to mineral spirits or lacquer thinner your are taking off some of the finish which you will have to re-apply. Try a hand rubbed polyurethane in a matching gloss to what you have. Or of course you can call a painter who could handle this for you and is experienced. Sorry to hear about the stains. Next year, keep those decorations on the window! :)
