Nintendo 3DS Top Screen Won’t Turn Off

Both 3DS screens work fine, except when I close it (and it goes to sleep) the top screen stays on. Instead of turning off it just has a lit up black screen and that drains the battery quickly. It also needs a battery replacement, but I want to fix the screen issue before I replace it so it doesn’t ruin the new battery. Is there some way to fix that screen issue without a full replacement?