I also have the same issue.. SP3 detects AC adapter wall charger but does not charge.
The update, “System Firmware Update - 11/7/2016”, would not install from /Settings/ Windows Update window.
My battery is stuck at 7% and if I remove AC charger, would shut down after few minutes.
PS3 works with AC adapter. My purchase date is Nov 2014 and I am out of warranty. MS store support center re-installed Win 10 and thought this might fix the issue. It did not. They did not complete the firmware update as it was taking too long and I had to leave. I tried to complete the firmware install at home and having issues with it.
any suggestion ? Thank you.