I got this problem with my LG G2 that it fell in the water once, I directly put off the phone. (It was still intact after falling in water).
Later I turned it on but the screen did not show up. Sound works, Vibration works, TOUCH screen works (no graphical stuff) and even if I call my self with another phone the LG goes off, vibrates, plays the ringtone and everything.
I sent my phone to Dynafix which is the repair center, they said it's not available for warranty, because its water damage and they declared the phone as "Unrecoverable". Which I think is pretty weird. I have thought of repairing it myself by buying and new LCD and Digitalizer.
(w w w . etradesupply . com/lg-g2-d800-lcd-screen-and-digitizer-assembly.html)
I have never done that though but with a good tutorial on YouTube and the right tools I should be able to do it. But before I take any action which may not work I want more info about this problem.
I made a video of my phone but can't post any links here, the name is: "LG G2 screen doesnt go on? [HELP!]"