As I mentioned the "Axxxx" designation is too broad and covers multiple model years. You can get the exact model number by entering the system serial number here:
Check Your Service and Support Coverage - Apple Support
Assuming the Battery is the problem, then disconnecting the battery from the Logic Board should allow the laptop to power on. Sometimes if you reconnect the Battery while the laptop is still powered on, the Battery may begin to charge. You must allow the Battery to charge at least 10% before powering off the laptop or disconnecting the charger, otherwise the Battery may be permanently damaged. If the Battery has been left completely discharged for a while, then the battery may be already be permanently damaged. Sometimes beginning to charge a Battery after having been discharged for a long time, the Battery may actually begin to swell, so you will want to keep an eye on the laptop for any signs of swelling.
There is a good chance the Battery will need replaced. If the laptop is still supported by Apple, then getting an Apple Battery repair is your best option since the quality of third party Lithium-ion Batteries is extremely poor even when purchased from a reputable vendor such as OWC. Only the 2015 model still has hardware support with Apple, unless Apple is allowing an AASP to replace batteries on the 2013, 2014 models for up to 10 years (sorry cannot find the link to the Apple article referencing possible battery replacement for possibly up to 10 years).
