My iPhone 6 ran out of battery and when plugged in screen does not show its c...
I've read somewhere that Lithium batteries have protection against over-discharging, they do this by breaking the circuit if the voltage drops too low to prevent further drain. Unfortunately, once this has triggered, you can no longer put charge back into the battery because the battery is disconnected internally, so no matter how long you leave the phone on charge, it remains disconnected and flat.
You only need to get the voltage in the battery to raise a percent or two to reconnect the protection circuit so that it will charge again and you can do that by warming up the battery. You may get away with leaving the phone overnight in a very warm (hot) place, such as on top of a hot water tank, however a more efficient way is to heat it up the bottom of the iPhone until it's quite hot with a hairdryer. Heat it for a good 3-5 mins so that the hear soaks right through the battery and it feels hot to the touch, this will raise the internal voltage enough to reconnect the protection circuit. Immediately reconnect the charger to the phone. After about 10-20 mins, enough charge should get back into the battery to fire up the phone and it'll come back to life.
Try this only if hard reset (holding down both home and power button until the screen turn on) fail to revive the iPhone.