Chosen Solution
I was repairing my New 3DS XL today, and somehow one of the small, black ribbon connectors broke off of the board. It was one of the non-ZIF connectors and while I was pulling the cable out the whole thing came off. The 3DS does not power on now (Except for a brief blue light and a pop sound) Is there anything that can be done about this? I don’t know if they are replaceable, but I would like to try if they are. Update (12/10/2018)
My phone refused to let me take a picture of mine, but I found one online that is the exact same model. I put up two pictures, the first is the connector just circled so you can see how it’s supposed to look, the second has yellow lines covering the parts that broke off.
Can you take a picture of which connector? Sometimes these can just be soldered back on depending on the severity of the damage.