Lenovo Laptop won't turn on unless plugged in

Good day! I am Independent Advisor Paul R. and also a Microsoft/Windows user like you and I am glad to be able to provide assistance to you today. I understand that you are having an issue with your laptop that is not powering on when not connected to the power adapter.
Is the battery indicator lighting up when you try to charge it?
Have you tried to disconnect and reconnect the battery from its bay then try it again?
Is there any accessories connected when you are trying to turn out your laptop when connected with its battery?

You can also try the following and check if it helps out.
Uninstall Microsoft ACPI battery:
Press Windows key + R. Type ‘devmgmt.msc’ and hit ENTER
Expand the Batteries category
Under the Batteries category, right-click the Microsoft ACPI Compliant Control Method Battery listing, and select Uninstall. Be mindful and do not remove the Microsoft AC Adapter driver or any other ACPI compliant driver
On the Device Manager, click on Action and then click on Scan for hardware changes.

Run the Power troubleshooter and disable Fast Startup:
Open Control Panel > type ‘power’ in the search bar
Select ‘Choose what the power buttons do’
Click on the option that allows you to change the settings that are currently unavailable
Uncheck the option ‘Turn on Fast Startup’ to disable the feature

Regards,
Paul R.