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I'm sorry to say that your camera is probably 'broken', if the screen remains dead and black or blank. But there are some things that you can try for this problem (aside from repair-servicing):
Try removing the batteries, and leaving the camera on a (dry, non-humid, non-dusty) shelf for overnight. Then put the batteries back in and try the camera again.
Then try cleaning the terminals in the battery compartment, after removing the batteries, first by rubbing off with a fresh pencil eraser, then by wiping the terminals off with cotton swabs moistened in rubbing alcohol, then letting them dry off for 5+ minutes with the battery compartment door open, then try turning the camera On again.
How long has the battery or batteries in the camera been in-use? If over a year, then you might possibly have a battery/batteries that are getting weak. Rechargeable batteries do get weaker with time, and eventually fail to deliver enough power to start up a device like a digital camera; they then need replacing. The replacement battery needs to be charged up for 6+ hours before its first use, owing to its having been on a shelf for a considerable time.
How old is the camera? in months or years since you bought it.
Has the camera been dropped or otherwise subjected to mechanical shock(s) in its lifetime?
Has the camera been operated in or subjected to, temperatures below 32 degrees F (freezing point) or above about 100 degrees F ?
Has it ever been subjected to a humidity higher than 85 % or gotten wet ?
Has the camera been operated in a gritty or sandy environment, such as a beach, a seaside, a construction site, or the like?
(If you would like to consider having the camera serviced, the question about how old it is (along with the other queries about how well it has been cared for) can be apposite to its warranty coverage status. That's why I ask about those points - having warranty coverage status means free-of-charge repair-servicing from Nikon, should that be the case and should it be necessary... and important point, I'm sure you can undertand.)
OK - I admit that I missed that point, that it is a waterproof camera.
You can have it repaired by Nikon, or by other companies that repair Nikon products... would you like a price quote on the choices? I may be able to obtain a price quote for you.