Since the internal construction of the 12C has changed so many times in the last several years, I don't know what is inside. It might be salvageable but you'll need to open it to find out. Here's how:
Place the unit face down on a soft surface. Remove the battery door and battery. Remove the the two small Phillips screws found there. Carefully lift up/peel off the four rubber feet. Remove the four screws. Lift the back off. Looking carefully at the right side of the unit, look for two small springs standing on end inside black vertical tubes. Remove them and set aside noting that the longer one goes in the tube nearest the display.
Now, have a look at the circuit board. If the unit has a small hole in the board behind each key location, great, you should be able to repair it. If it is a solid board with no openings, it's toast.
If you find the small holes behind each key, you'll need a method to get a few drops of isopropyl alcohol or contact cleaner (no silicone!) inside the hole then press the key a few times to flush out the key contacts. An eyedropper or pipette of some sort will do in a pinch. Repeat at least 2-3 times.
Install the springs and reattach the back with the six screws and reinstall the feet. Should be okay. Repeat the process if needed.