[Avro_Arrow]

I couldn't see anything that jumped out at me in the pictures...the only thing I can suggest
at this time is to carefully check the USB and DAC chips for anything stuck in between
the pins or, more likely, a dry solder joint.

 

[cobaltmute]

Check all the traces that go between the two chips for shorts between pins and ground.

 

[Oeufdepoire]

There's no shorts between the traces between the chips and ground.
 
I've changed the output jack one more time, still no sound.
All the contacts between U3's pins 1 and 16 (the lineouts) and pin 4 (line ground) are OK : the contacts, the traces, the resistor, the caps, the jack, the drivers, all this is correct.