AC Adapter Plugged in - Not Charging/BIOS Update

I am trying to troubleshoot why my AC adapter is not charging. According to Device manager, it is working properly. Posts indicate I should try to update BIOS, however my battery is below 10% and it will not allow me to update it. What can I do?

Also, I read about removing a battery and charging it. How do I do that?

Please help before my battery dies altogether!