Why Won't the top screen of my 2DS turn on?

Hi!

The could be a problem with your upper screen ribbon cable.

If you bought your console anew, I'd recommend sending it in for a warranty-repair, the place you bought the console from will either replace it of fix it for free.

If not, I'd suggest taking it apart yourself using our guide here. Once you get to the motherboard (at 1:14 in the video), check all connections, make sure everything is tight in place. If you can't tell, disconnect the cable in question and reconnect it just in case.