Re: acer 1670
Start with the easy things, try swapping the battery with another and see if there is a change. Do a BIOS reset and possibly update if one is available. Check that you don't have any odd "power manager" type apps installed on your computer. Check that you have defaults setup in your "Power Options" in control panel. You can edit the power plans and select reset to default.
Next, you can use a multimeter to test the terminals on the battery plug to ensure power is being delivered to the battery so that it may charge. If you or someone you know (or even a local shop) is comfortable disassembling the laptop, you can test the solder points where the DC jack attaches to the motherboard to ensure the DC jack is not damaged and in need of replacement. If none of the above resolve it, it's possible your motherboard is faulty. That was the case for a laptop I had that was doing what you describe.