Remove all contents from your cabinet and smell each one. Throw away any perishable items that don't smell fresh. Depending on the severity of the odor, wrap items in plastic first. Temporarily relocate items that smell fine.
Wipe down the inside of your cabinet with a combination of vinegar and water. If there is a specific food stain in your cabinet causing the smell, allow a puddle of vinegar and water to soak the stain for a few hours.
Leave an open bowl of white vinegar in your cabinet for a week. If you need to store items in your cabinet while working on the smell, pour white vinegar into a jar and poke holes in the lid, so the vinegar is able to absorb the smell through the jar.
Place a saucer of coffee grounds in your cabinet, if the white vinegar doesn't work. If you can't leave the coffee grounds in the open because you need to use the cabinet, pour the coffee grounds into a jar with holes poked into the lid, or wrap them in a cotton sock, T-shirt scrap, paper towel or some other absorbent material that will allow the coffee smell to absorb the bad odor.
Leave an open container of baking soda in your cabinet. Baking soda will absorb any remaining odor over the long term, and keep any new odors from emanating.
Replace the cabinet if you've done all you can and the odor remains. For a cabinet made of unpainted wood, or another porous material, you may never be able to remove the smell and replacing the unit may be your only option.
Find a new place to keep your potatoes. In the future, pay attention to when your potatoes get old. Throw them away when they're no longer fresh.