I think this is a problem related to the power that is being delivered to the screens.
I never had this problem until a few days ago when a friend of mine told me his 3DS XL wasn't able to boot.
The console was able to boot on the Luma configuration menu without issue, but if it managed to boot normally, only the backlight of the top screen showed up, (almost, except the very corners that looked awful) nothing could be seen even if it could on Luma's configuration. Also, the bottom screen looked more saturated and overall white, but both screens were fine.
The problem here was that a bad use of the device lead to the flex of the 3D slider and speakers to break so slightly, with this, the console could only power on on certain angles and without moving, even with the Luma configuration menu.
My theory of what could be happening:
Don't take this too serious, chances are that I might be wrong, but what could be happening here is as simple as the screens or the things that they depend on (such as the slider or speakers in this case) might not be getting enough power to work properly. I think this because the flex (of something that had nothing to do with the screen states) that was broken likely had this exact problem and it made the 3DS to work as you two describe. This would explain why it worked on Luma's configuration and DS games while not in the 3DS menu.
Even if at least one of you was able to fix the problem already, here are some thing anyone facing this exact problem can try in the future:
- Ensuring the battery is fine (even though, I don't think a bad battery might be able to cause this issue).
- Opening the 3DS and look for visible damage or loose connections, including flex.
- Cleaning the inside of the 3DS carefully.
