Finally I found enough time to open (again) the laptop.
After I've studied the electronic scheme of MB, I realised that the short that I made was totally wrong.
If I number the pins like this :
12 gap 345
then the needed short was...
Thanks @Idiomatic : I will follow your suggestion and I will re-solder all audio jack pins. Hope this will help. If the resoldering will not help, what should I try to bypass the headphone jack?
Another solution would be to swap the 3.5...
I have the same problem as you : my Dell 9300 stops playing sounds. If I put some pressure on the right side of the keyboard, sound starts to work again.
I've disassembled the laptop and extract the MB to check the audio out...