There is a super secret button I found that fixes this. I don't understand what this button is for but once you add some tape inside to permanently depress this tiny button, the computer will start up again. You have to unscrew the bottom and pop off the plastic housing. Next to the right hinge (looking at the board with hinges on top), you will see a tiny little black switch box with a minuscule spring switch. Press the switch and power returns. Wad up some tape and put it where that switch meets the plastic housing. Then replace the housing and screws. You should be golden for a few months until the tape wears down.
Anybody know where to buy replacement back covers for this original 3DS model? I’m finding that a lot of used 3DS’s from this era have 3rd party battery packs and the original cover is lost.