Alright I just had this problem with my 3ds new xl, I've been letting it sit after playing around with it for a bit seeing what I could do, noticed it took unusually long to hard off when i held the power button. Today I turned it on and noticed the red blinking light, it to was blinking slowly.
So after looking threw these I chose the simplest one, and huh. I just left it on for like 5-10 minutes while having a smoke.
I seem to have caused some sorta error in the bootup that just caused it to boot really slowly, I imagine an older model woulda been even longer. It seems to have worked through whatever error that was filling the cpu now that its got to the homescreen.
I also know it happened right after it was charging and we flicked a bunch of breakers on and off a few times, we were checking wiring. Oh and my sd is 256 gigs I could see that causing the occasional problem on boot.
Alot of these other solutions like taking out your battery, performing different kinds of resets for clearing you're caches. I'm sure taking out my battery or letting the battery run dry today woulda fixed it too.