Hey,
Sorry about your Note 3, that is a real bummer.
First thing is first, water damage is tricky, and sea water is full of impurities. Take the phone apart, and treat the motherboard for water damage. If you don't have the proper facilities, a good scrub with isopropyl alcohol (at least 90%) will certainly give the phone a better chance of survival. It is possible that corrosion has set into your screens ribbon flex, or the connector on the motherboard itself.
Unfortunately, since the device was turned on, and plugged in, there is a good chance you will need to replace the LCD, and since the device had power sent through it after being wet, the display may never come back. Certainly better to try though, as you may have a perfectly fine device that just needs a new display!
Good luck.
-Samantha S. Device Savers