Does it say "plugged in, charging" or just "plugged in"? If your laptop shuts off as soon as you unplug the charger then it's probably a dead battery. If it's still capable of using battery though, just not charging, then you might have some more serious issue.

You can also try taking out your battery (while laptop is unplugged and off!) and clean the connectors with a dry tissue. Sometimes dust tends to get there through the cracks and block the connection.
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Also you might just have a software bug? Highly unlikely but still possible. You can check if that's the case by using third party app like BatteryMon or something