First of all, you have to know how to open the top shell. The solution is shown here: How to remove top shell of New 3DS XL 2015?. Now if both left and right speaker works(by any chance because of the first reason) , the ribbon cable should be completely fine, and you probably just didn't align the exterior slider and the interior one correctly. Now in this image , inside the red circle is the small circuit board that connects to the speaker. You can see there's a little black thing sticking out. That is the "interior" slider, and in the yellow circle which is the "exterior" slider(not the perfect angle but meh you can see it), you can see there's a place for that little black thing to stay. This is how the interior slider move when you move the exterior one. To align them, you simply just have to move the exterior slider to very bottom and do the same to the little black piece, then place that small board back and make sure the little black piece is aligned perfectly. The same is to be done at the other...
First, is your console cracked?(not physically, but Gateway, A9LH etc.) This could be the main reason for your situation Second, there may be some issues with the wifi board, check the connection of it and see if the problem persists. If it does, consider about contacting Nintendo and see what they can do for you or maybe another person will be able to help.
I know you had checked many times, but did you plug in the ribbon cables correctly? Some cables' copper side are supposed to be plugged to another side of connector. This is the only solution this inexperienced person can think of, no guarantee this will work but it's worth a shot.
Now if you mean this piece it's very simple. First remove these 4 plastic pieces that are circled here that are hiding the screws (nope nothing under rubber stopper this time), then remove the screws. After that simply pry open the shell from where the red circle is and you're free to go.
This problem can be as simple as the battery died or ribbon cables inside getting loose. And although very unlikely, there could be some issues with the motherboard as my friend's new 3ds xl had the same problem and that's why his console won't start.