The last thing you should do when an electronic device, such as your D4, gets wet inside is power it up. Instead, you should remove all power sources immediately and not provide any current to the sensitive electronics until the device has been thoroughly dried for several days. Impurities in water (yes, even rainwater has impurities in it) will conduct electricity and can short out the micro-electronics in the device.

If the power source is removed immediately and the device is allowed to thoroughly dry, there's usually no permanent damage or corrosion if there are no salts present.

We're not just talking about table salt (sodium chloride) or sea salt (NaCl + several others in trace amounts) here, but rather any chemical compound considered a salt, such as Potassium Dichromate, Copper Sulfate, or Calcium Chloride. If there's very much ionized salt in the water the device is probably a lost cause. Even if the device doesn't die immediately, the salt deposits left inside after drying out will eventually corrode the internal electronics.

If camera service centers, particularly the official ones owned by the manufacturers, get so much as a whiff of evidence that water has been inside a camera body they will say the damage is not covered by warranty. If they get a whiff that salt water was involved, such as by seeing green corrosion on external screws, they often won't even open the camera up inside their facility.

At this point you don't have much to lose, so you might try the technique used by the "Nikon Repair Center in Taiwan" (who clearly disclose at their website: "We are not an official service provider for Nikon Corporation") to fix an expensive Nikkor lens that had been dropped in the ocean.

We've had a few other questions here that address water damage:

What could cause exposure problems after my camera got wet?
Can I do anything about a Nikon d750 taking 5 minutes to power on after taking saltwater damage?
DSLR in sand and salt water
Why does my autofocus sometimes set the aperture, after the lens was in the rain for several minutes?
Water-damaged Canon EOS 550 giving Err 70