I have an Acer Aspire E1-571-6837. It will not charge the battery out run the computer with just the power supply. It is a new

If this is a new laptop, then you need to contact the manufacturer, or the place of purchase, as it should be under warranty and should not be giving you such problems.

Now if the battery or the charger is new (and not the laptop) then you may need to test the other part (if laptop is new check battery and vice versa).

It may well also be the charging circuit, which should be on the motherboard.
 

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