Then, i remove the screen (2 screws), so that the motherboard and the connecting pins are easylly accessible.

In the second picture, you can see that near the pins, there is a "+" and a "-" sign. Here, by gently pressing them with a screwdriver, I noticed that one of them was completly loose. That is the reason of the problem.

Then, it is simple to fix it by soldering the loose connection.

The problems comes from the fact that the battery pins are directly solded to the motherboard, therefore the force exerted to maintain the good contact with the battery is applied to the soldering, which may eventually brake.