Ever stored flashlights, toys, cameras, etc. without removing the batteries, only to discover later that the batteries leaked and your electronics now won't work? They might be saved if it hasn't damaged a circuit board or something.
There is a good chance you can save your product by using vinegar. That white powder is potassium hydroxide, which is a form of lye. It's very alkaline and caustic, so you don't want it to come in contact with your skin.
Wear gloves (and possibly goggles for safety). If there is any loose powder, dump it out first. Using a q-tip, dip the cotton into the vinegar and squeeze off the excess so it won't drip into your product. Rub around all crusted areas. If you have room, you might employ a toothbrush. The vinegar will dissolve the lye buildup as you work. It may take some time for this to happen; keep dipping and squeezing and rubbing. Some areas might benefit from rubbing with a pencil eraser.
When you get it all clean and absolutely bone dry, insert new batteries and check the results.
I saved a police scanner doing this some years ago.