I have similar problem,
Just transfer my laptop to a "new" (ebay) top case with new battery. this is the power profile data:
Charge Information:
Fully Charged: No
Charging: No
Full Charge Capacity (mAh): 9267
State of Charge (%): 36
Health Information:
Cycle Count: 7
Condition: Normal
the battery icon shows power cord connection. but says battery not charging. I have tried SMC reset and nvram reset.
My laptop is a MacBook Pro retina 15-inch late 2013.
Fan are working ok, keyboar back light ok, Light sensor and auto screen regulation ok.
Just the freaking battery not charging.
Hopefully won't have to get a new battery again... (at least were 60 bucks)