With no knowledge and no real burning marks I wonder why the try? It sounds to me that when even you did found something you still are not able to fix it.

But this pic is the battery connection?
https://imgur.com/5ZUG6vC
Looking at it it seems there is a SOT23 diode, FET or transistor on it

This pic: https://imgur.com/6COrcDC
Going down from display, 4-pole connector, switch... Right under the switch I do see someting like a voltage regulator., that one it probably defect.