This seems similiar to the Black Screens of Death with background music
brick that occasionally occurs on the New 3DS XL system.
Those who experience this specific brick have,
- black screens and working sound in HOME Menu
- both working screens and sound in Recovery Mode
The cause of the brick was found to be faulty camera module. The short term solution is to disconnect the camera ribbon cable; long term would be to replace the cameras.
Because your brick is different,
- black screens and no sound in HOME Menu
- black screens and working sound in Recovery Mode
, you might have two separate components that are faulty (ie, might be something else other than just the cameras).
The image of your motherboard that you linked at:
, doesn't point out which two plugs you're referring to.
You may want to study what each part is at: