As I wrote, I've opened the back cover and checked the batt voltage and and I managed to "unstick" the battery from the back of the screen (it was really tricky, 2 strips of a white double sided sticky tape): it looks ok and the voltage is 3.88V at 100% full (as showed in the device screen when connected to AC).
It would have been good news if the batt had been dead, cause easy to replace it. But it doesn't seem to be the case here.
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