Why won't my Nintendo 2DS power on?

It would be helpful to know more about your problem, but for general reference this troubleshooting guide has some information on your problem.

Your ds is broken or simply remove the back and check the battery for anything weird this is what happenrd to my dsi before you do this try charging it for ,24 hours if that doesn't work do what I said above.

I had this same issue. It seemed to work again after I removed the back, reseated the battery back in, but the was a metallic rattle in the inside. When I took off the back fully there was a silver colored metal plate that had come unsoldered. Anyone know what the function of that plate was? 2ds turns on without it in there but need to know if it could cause issues if not put back on. Don't want any hazards.

The 2DS might be in sleep mode while it's off.

I just opened the battery case part (top two screws - size 00 Philips), took a pencil eraser and "lightly" cleaned the terminals of the battery. Dropped battery back in and it works fine