Hi,
When the charger is unplugged the Zembook switchs off
This is strong indication that your battery is dead. Of course it could be some problem in onboard power supply circuit, but must likely it is bad battery.
, despite the battery indicates 100% charged.
In some case it could be really charged but may have bad connection or high ohmic resistance and dies immediately you disconnect charger. I'd download CPUID HWMonitor application or equivalent. It may be able to show battery wear level stored in battery controller. HWMonitor battery wear level is shown correctly for UX331U
Edward