Good news, I swapped the board into my N3DSXL and it worked! So I know the board is fine, it could be any component that could be causing the problem. I don't think I have the time or patience to replace each part one at a time to see what's causing the issue. Do you have any advice? The owner told me to was exposed to a lot of sunlight before it stopped working, if that helps at all. Right now we know the motherboard, SD card reader, circle pad, and battery work.
Hmm... Hard to say. Nice that the motherboard is alive, though!
It's unlikely that it's one of the displays, since then, you'd expect a shut-off with speakers popping and possibly a white screen flash. But the possibility that one of the displays has failed in a way that causes the system to freeze on the blue light also cannot be excluded.
It might be one of the other components of the top lid, such as the cameras, super-stable 3D sensor, volume / 3D depth sliders, speakers. I'm not sure what the exact arrangement of those is on new3DS systems, but it could be one of the ribbon cables that you mentioned were looking slightly off. If one of those components is being faulty, it could be that the 3DS OS is locking up and unable to finish booting, instead of the system shutting off at an earlier self-test stage. I'm not too sure about the specifics of new3DS systems, compared to old3DS.
I'll ask: do you know if this 3DS is modded? If you're not sure, you can find out while the motherboard is working in your 3DS unit. Try pressing L+DPad Down+SELECT in the OS to bring up the Luma3DS menu, and/or try holding START or SELECT while turning on the system (pressing the power button), to bring up either the Luma3DS configuration menu or the Luma3DS chainloader.
If you're now sure that the 3DS is modded, you can try, with the motherboard back in its faulty unit again, holding down START or SELECT while turning the system on. If the 3DS OS is locking up and unable to finish initializing because of one of the components, the Luma3DS pre-boot menus and utilities such as GodMode9 might still be able to initialize and display their menus, since they're much simpler and have no need to initialize all of those components.
On the new3DS XL, you also have a daughterboard, and the Game Card slot is also an external part. On old3DS, those parts were integrated directly onto the motherboard. They might also be critical system components - the ribbon cable connecting to the daughterboard is quite wide, and if I remember correctly, the daughterboard also had some integrated circuits of its own.
It's probably a good idea to try swapping those parts.
You should be able to speed up your testing by not completely replacing those components for every test, but just connecting known good parts loosely, while the existing parts are still mounted to the shell. However, you must be very careful when doing this. Don't test things this way for a prolonged period of time. If you're going to place a circuit board on top of the existing one, you have to protect from short-circuiting them. Insert a small piece of cardboard or something in between for isolation. And you'll probably have to keep holding it all down while trying to power the system on, to prevent it from falling apart. Having to hold the battery down to the battery contacts/terminals by hand also doesn't make it easier. You're doing it at your own risk and you have been warned.
If one of these quick component-swapping tests reveals that the system now powers on, don't bother testing it further when you're probably already using both of your hands just to keep it all together. Remove the battery, and proceed with the full replacement procedure for that component.
If you prefer to stay safe, you'll have to fully replace each component just for testing, which can take a lot more time. Of course, you can still save time by temporarily mounting a component like the daugherboard on only two screws, instead of all of them.
This method can be used for testing the top-lid components too, if you have spare parts (cameras, sliders) that are loose and not already mounted inside of a shell.
