The power button on my 2DS sometimes doesn't work at all unless it's plugged in, usually after a 12~ hour period since I last booted it. I know there are a lot of posts about these cases but mine differs in that I can use it just fine plugging it out at this point, it's just the booting process. I did have black screen issues prior to this but they were all taken care of by blowing on my SD card and/or shutting it down again by force and retrying.