try leaving the phone unplugged without the battery for a day or two then put it back in and try to power on... plug into a computer and wait 1 minute then press then hold power button to try to get it to turn on assuming the screen died on you, (see if you here sounds or vibrations)if i will still not power up try taking it apart and checking cable connections for damage...
Take off the battery then place it back in. Does the LED turn on when you plug in the charger? Even with the screen off, can you hear the startup music when you turn it on? More than likely the screen digitizer is unplugged or damaged. If you think you can tinker with removing and replacing small parts, it should be an easy fix. LG G3 Screen Replacement - iFixit
I replaced mine before (work accident). Or you can send it to get it repaired at your local phone repair shop.