'''Software solution below:'''
I had the same problem, and it is a software problem, not hardware: Battery 1 was fully charged, Battery 2 had 5% charge, but could never get charged. (my battery 1 is not removable).
Here is how I solved the problem:
* Go to your Windows '''Device manager''': Under “Batteries”, you will have two times “Microsoft ACPI-Compliant Control Method Battery” ==> The first one is for battery 1, the second is for battery 2.
* If your battery 2 is not charging, then : Right-click on : “Microsoft ACPI-Compliant Control Method Battery” of '''battery 1''', and disable it. Then unplug and replug your charger into your laptop ==> Hop!! your battery 2 is “charging” now. You can enable back battery 1 (battery 2 will continue charging).
* If by doing this, you still have your battery 2 not charging, high chances you have a '''Hardware''' problem