Hi everyone , I have recently joined this forum because of this issue with my Zbook 15 G3.
Same problem : led on the power button blinking / flat battery and can't turn on the pc.
I saw on youtube a video about this same issue , and shorting a capacitor w a pair of tweezers solved the problem 4 me.
I wanted to share with you my experience hoping it is helpful 4u too
The capacitor I shorted is the white one under "PQ56" written on the motherboard ( see picture ) .
Now my zbook is charging fine.