Hi,
Here are some troubleshooting steps that may help ins solving that issue.
- Start by removing the battery and booting it up without it then once booted up put the battery back in and see if it will work without the AC adapter connected.
- If these doesn't work try to uninstall/reinstall "microsoft acpi-compliant control method battery" from Device Manager.
- If these still will not work I would suggest changing the battery but the problem may also lie inside the laptop where the connector for the battery meets the motherboard. If it's not connected properly it won't be getting the voltage it needs to power the laptop.