I did not encounter this problem with a New 3DS XL, only with a 3DS XL. In my case, the fault was found in a flex cable linking top to bottom of the console. It was the one handling the speakers.
You could have the same problem with a bad connection to one of the flex cables. I would search for one of these problems, in this order.
Disconnected cable (easy - just reconnect)
Corroded contact on the ribbon cable (easy - sand & cleanup with IPA )
Corroded contact on the board connector (medium - use toothbrush to clean slowly with IPA, use a pick to clean contact, very carefully)
Broken cable, either fully or partially (hard - buy and replace connector, tutorials exist | very hard - remove and micro solder traces before reinstalling)
For the last case, you'll need to disassemble the top screen completely, which is very tricky, and comes with a risk of additional damage.
I was in the last case and chose to microsolder the 3 broken traces. Would not recommend to do it without at least a microscope.