D3 packed in
I shot a valleyball game under light rain with my D3. After that my LCD has some marks from the inside that I couldn't clean.
I brought the camera to Nikon Canada service department. The technician told me that the inside coating of the LCD was damaged by the humid/rain.
This means, humid could get inside the D3.
For your case, I would suggest you to remove the battery, and use a hair blower aiming the battery chamber. Hopefully this will dry up the inside somehow, and bring the camera back to life. If this doesn't work, then having service from Nikon is a must. And you better do it asap.