Why Does My Lap Top Turn Off When Not Plugged In?

The only possible reasons is the batteries. Though the battery shows that it is hundred per cent charged but still the back up time of the battery is very short that it turns off as soon as the charger is removed.

The similar case you might have seen with the cell phone batteries. When you charge the batteries it shows hundred per cent charged and soon after the cell turns off within no time.

More than likey you probably need a new battery...this usually happens when you contiously keep your computer charged even after its reached 100%