Xbox doesn't boot, but the controller ports are powered

Hi,

I have a problem with my Xbox (1.6)

When I press the Start or Eject buttons, the light does not come on but the controller ports are powered, but only for 1-2 sec. I have disassembled the xbox, to see if it wasn't coming from motherboard oxidation, it works. Then I put a product for button oxidation, but still the same problem. I saw on the internet that it could come from a transitor (MMBT3906LT1 ). Before buying it, do you have any ideas?

Here is a video : https://youtu.be/HZzzelYD6xY

P.S: If I keep pressing the buttons, the ports remain powered but no display, no sound, no dvd player...