Finally, I solved the problem by changing the upper case cable. Unfortunately I couldn't buy on iFixit. I found it there: https://www.amazon.it/gp/product/B01MSH3... And then followed this guide: MacBook Core Duo Upper Case Cable Replacement Thanks for the help !
Be really careful! I broke the connector easily and had to replace it.
It is out of stock on iFixit. I found it there: https://www.amazon.it/gp/product/B01MSH3...