3DS won't turn on

Hello there,

so today my 3DS just decided to not work anymore for some odd reason.

3 days ago the side of my 3DS got a big hit, it accidently fell like 30cm deep but it didn't seem to be that bad, because it was on when that happened and it would still run normally. So over the last days i just left it on like always and charge it occassionally.

But at some random time, i don't even recall if i had to reboot it or just turned it off, i wanted to power the 3DS on again, but it didn't work.

Problem:

-3DS blue light comes on for 1 or less than 1 second

-Turns off

-No so called "popping sound", just turns off and can be turned on instantly with same result

-It can charge as usually with or without battery, also the battery and the contacts dont seem to be bend or damaged

So i'm not too sure if the fall actually caused this, since it seemed to work beyond that point, but now i encountered this problem here. Any ideas what i could do?

Sending it in to Nintendo would probably cost me 80 bucks i've read, so i could just buy a New3DS XL if i had to.

I hope someone can help me and thanks in advance!