Not Power on problem

Looks like your battery was not actually charging, maybe it's broken. If you're sure that all cables are ok, you have to open one of the headphone containing the battery and check its voltage in standby, and check if it increases on charge and speed of increasing.

For example: if your battery stb voltage is 3.5v and several minutes after charger connected it increases to 4.2, that means the battery lost it's capacity and needs to be replaced.
If your battery voltage not increases, there's a chance that problem is in charging circuit (usually it uses SOT23 mini package chargers on motherboard) or in USB socket, traces, wires etc.
If your battery voltage in standby is less than 3.0 V or equals 0 V, there's a chance that battery is depleted completely and requires changing.