Hi!
It actually sound like there is an issue with the top screen it's ribbon cable.
I would try and test a new top screen and see if that fixes it (most likely it will).
I'm not going to lie, it's a real job to get it replaced, but worth it!
Guide: [guide|25070|Nintendo 3DS XL Upper LCD Display Replacement - iFixit Repair Guide|new_window=true]
If you need anything else, please let us know!