Hi,
It seems like your battery is faulty already unfortunately but here are some troubleshooting steps that may help.
- Start by doing a hard reboot, remove the battery and unplug the AC adapter then press and hold the power button for 20 seconds then put everything back together and see if it will stay on with just the battery.
- If it doesn't work remove the battery and plug in just the AC adapter and see if it will stay on because if it does that means the problem is with the battery.
- If you're comfortable opening your laptop I would suggest checking the terminals that connects the battery to the motherboard if there's any broken solder that stops your laptop from powering with just the battery.