I don't know if the iPhone 6 would still turn on being connected without a battery, most phones turn on without a battery connected. I would take the battery out and connect to the charger, place your hand on the logic board and if you feel any kind of warmth coming from the board then you know the charge port is working. Keep me posted, it could be the charge port needing replacement, also check for any dust or lint inside charge port and clean it out.
Sounds like the battery took a sh!t, it never hurts to order a new battery online either on EBay or Amazon for your phone. Make sure you find a OEM battery. Also i recommend always charging your phone via the wall not the computer. A wall charger generates more charge power, i would hard reset it following these steps and then plug it into the wall and let it charge, if same problem occurs then you need a new battery or at least a used one that has been tested http://www.hardreset.info/devices/samsun...-i9060-galaxy-grand-neo/
Make sure you put the screws back exactly where they came from ESPECIALLY if they are of different sizes, i remember back in the day i screwed up the motherboard by putting a slightly longer screw in where a short one was suppose to go and it peirced the board enough to where the display showed up white with a bunch of colors and lines, good thing the board was icloud locked anyway.