Answer to: My Nexus 6 battery will not chargeYour ribbon cable may have come loose. It is rather difficult to connect. Double check the connections on both ends. Does your power button work? If your power button does not function, then it is definitely the ribbon cable.
Answer to: My Nexus 6 battery will not chargeIf your phone is on and remaining at a constant battery level when plugged in (not charging but simply maintaining a charge level)... YOU NEED TO CHANGE THE RIBBON CABLE BETWEEN THE ON/OFF SWITCH CABLE AND THE MOTHERBOARD, as stated above.. It is available on ebay. Be gentle because the motherboard side connection to the ribbon cable is a weak point. There is a black rubber tab holding the cable down where it connecta to the motherboard. On the other end the ribbon cable connects to the ppwer and volume rocker cable. If you have this no charge issue, you likely have a power or volume button problem too because these buttons connect to the motherboard via the damaged ribbon cable.