Is the battery old? Are you able to check the # of charge cycles on the battery? The power adapter is the original and suitable for use with this laptop?
If there is a doubt on the above details of the battery - test with a known good battery first.
Do you have a multimeter to check on the voltages? If yes, meter in dc volts scale (20v or higher is ok). Carefully measure the voltages to ground on each pin of the battery connector while the power adapter is attached to the logic board.
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