If it isnt the power supply my money would be on the connections of the power plug and the PCB in the laptop, the regulator board (if discrete) or the motherboard if the power regulation is not a discrete board.
It happened to me wereby the charger stopped charging but charger was fine, the battery ran down and stopped. Fortunately for me the laptop was still under warranty - final months of a 3 year warranty.
Have you tried a known, charged, battery in it?
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