|Don't boot the laptop, let it charge up the battery. Allow about 4 hours for charging then boot the laptop and see if the battery level has changed.|
If the adapter light is not on then the charger is faulty. If the charger is not the same as the one that came with the laptop then it is not compliant.
Sometimes the power jack can get damaged if the cable is knocked harshly, you might have to take it to a service center if no other resolution works for you.
You should not run the laptop with the charger on, the charger is just for charging the battery when the level drops to about 10% then you charge it while still using the laptop but you need to turn off the adapter when the battery is fully charged (or 99%).