Laptop won't stay on unless it's hook up to the charger

Double check to make sure you battery is seated properly first. But going off your description of the problem you are having a new battery would most likely fix the issue since it works fine while connected to a charger and shuts off after removing the charger. This does sound like a faulty battery and I would recommend replacing the battery to fix your issue.

Your battery may need replaced. Until you can get it replaced, just keep it plugged in while you're using it and it will stay on.