This does not sound good. Popping sound when turning off usually means a hardware component is not found or does not respond properly (mostly ribbon cable issues). Hardware troubleshooting the N2DSXL is harder than the other models. Things to try:
- Turning on while shell is not fully opened (only to the first click or even less).
- Don't try booting a 100 times when hardware issue could be the reason. The immediate ("violent") shutoff is not good for the motherboard.
- Check if all ribbon cables are seated properly (or if any cables and/or connectors show obvious damage).
- Refer to the ifixit guides.
- N2DSXL requires a triwing/tripoint screwdriver to open and the shell is "clicked" together.
- When separating the two halves pay attention to the cables that are still connected to the motherboard.
Such problems can occur after accidentally dropping the console or spontaneously (wear and tear). In my collection is an example for the latter case. A lot of usage has damaged one of the ribbons going to the upper screen assembly over the years. The O3DSXL will not turn on when fully opened (and make popping sound) or will turn the upper screen backlight to the maximum regardless of the settings.
A few days before the real problem "cannot turn on" occurred I had a lot of random crashes (ErrDisp) while playing.
Comment: Replacing the upper screen on the N2DSXL is hard (they used a lot of glue).