No power, no charge. Makes a popping sound - fails to turn on.

Sounds as though you've got a bad battery fuse (charging light issue) and a small cut in one of the three ribbons that come from the top portion to the bottom portion in the hinge (popping sound).

The cut ribbon is a common problem and can be replaced but is a bit difficult, requiring some patience. Follow this guide to fix that problem: Reemplazo del conjunto del altavoz de la Nintendo 3DS This guide is for the older 3DS but should be sufficient to help you replace the speaker ribbon (or whichever ribbon is damaged).

The charging light issue may be a bit more difficult to figure out. Check your charging port to make sure it's soldered to the board properly. Locate the 2 fuses and ensure they're still working with a multimeter on continuity mode and ensure your battery is good.

I hope these help and good luck fixing it.