Instead of mechanically cleaning the contacts, I usually neutralize and chemically remove the existing corrosion with ordinary household vinegar. Any type works. I put some on a Q-tip and dab it on the corroded contacts. It will bubble a little bit and react with the alkaline battery corrosion. If there's a lot of corrosion it might take a couple Q-tip aplications to neutralize and remove it all. Sometimes a little bit of the neutralized corrosion will remain in areas where it was thick originally. A fine pointed dental pick or a toothpick can usually flake it off easily. After you get everything as clean as possible, dry the contacts off and use another Q-tip to wipe a small amount of dielectric grease on them. This reduces the chance of the problem happening again and the batteries will also have the best chance possible of getting good clean contact. Then reinstall the batteries and see if it works.
80% of the time that's all I need to do. The other 20% of the time, I have to take it apart more to find and fix additional corrosion damage. This often includes shortening and resoldering a battery wire lead because the corrosion has traveled to and eaten through the end of one of the very small gauge wires.
