According to this, the popping is a symptom of a failed system check on boot:
https://repair.wiki/w/New_Nintendo_2DS_X...
It states there are 4 components that must be validated: Upper LCD, lower LCD, inner camera, and battery. If any are damaged (or their ribbon cables, or ribbon cable connectors) it produces that popping sound.
Note that the ribbon cable connectors for the lower LCD power and RF antenna are NOT ZIF connectors like the rest. Lifting the "latch" on these breaks them such that they do no longer make a good connection. This is a common issue.
"Five ribbons must be connected to the motherboard to get it to boot to the home menu. If any of these are not connected or are damaged in a way that the system detects as incorrect the blue light will turn off and the console will not boot. These five are the Lower LCD, Lower LCD backlight, Upper LCD, Inner Camera, and the Battery (see Fig. 3). Only these five need to be connected for the system to start."
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