You have the charger, battery and motherboard. In the shop, if we are lucky we have another laptop of the same model but we use a Volt meter to see if the battery has any charge. If you measure Zero Volts on all combinations of the pins the battery has failed.

You also have to be aware of history. That is, a few years ago because of laptop battery fires the designs changed. Chargers and more changed so if you don't use the maker's charger you might see the issue you are writing about. And even then, if the charger has a specific failure it can run the laptop but not charge.

Then you have the motherboard. It has the remaining charging circuits that can fry if folk do odd things like slam in the battery when power is on.

Finally you have cables, contacts and more to inspect.

It's not a simple issue to troubleshoot.
Bob