Without knowing what's on the surface of the existing cabinet, my first preference would be to scuff sand to where you have some porosity, and use Titebond II with cauls or clamp so that you get even area pressure across the surface. If that isn't possible, and in many situations it isn't, use a solvent base contact cement, and follow instructions. Cut your piece slightly oversized and trim off after laminating. Use a slip sheet of formica or thin plywood, or even a series of dowels to keep the two parts from touching while you line them up. Allow for good ventilation, and after laminating, press down with the edge of a block of wood or tap with block of wood and hammer to get good contact.
You may want to check out the new glue from Loctite it's great stuff and you can clean up with water
I tried a tube last week and it worked out great on 1/4" plywood, it's not cheap but it works and it's fast.
I got the tube from Home Depot
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