Chosen Solution
The Thinkpad is properly plugged in at both ports but is not building a charge at all.
Test the power cord with a multimeter like in this guide. Testing Power Cord Continuity Then I would also test the power adapter is it is working with the multimeter How To Use A Multimeter If both test work fine then you know that your power adapter is fine and working. You should also look at the power connector on he laptop so it is not loose because then the soldering might not lead the electricity. Good lock in testing.
Try replacing the battery or buying a new charger.
