I have the same problem. This is exactly my problem. I decided to install the CFW on my N3ds XL last Monday and everything is good. Im on 11.16 btw. but today I opened my N3ds xl to change the analog stick after I put it back everything and I turned on I noticed it just stuck on blackscreen although there is a blue light. I left more than 20mins and it still in blackscreen with blue light.
I removed my SD card and it works perfectly fine. I tried different microsd they are all in Fat32 format but none of them work. SO IN SHORT - MY N3DS XL ONLY WORKS WITHOUT SD CARD. Please help
Did I brick my N3ds Sd card slot? or is this a bug on 11.16?