Original post by: Brian Wood ,
Open your iPhone 6 up and disconnect the battery. Disconnect the lcd, digitizer etc. Reconnect the lcd, digitizer etc. and plug it into the charger without the battery connected. Does it boot properly now? If so, the issue could be a bad/damaged battery from the fall. I know it was a small drop, but anything is possible. If its doesnt boot, unplug the charger and reconnect the battery. Now try to turn it on. If none of this works, there is a good chance your screen has gone bad. I know this doesnt explain the charging issue or the fact that it was working then blacked out, but I've seen bad screens cause all types of issues.