iPhone 5s keeps crashing while not in use

Hello there~

So a while ago, I dropped my iPhone 5s and it broke its entire display. My father-in-law got it fixed for me and they only replaced the display with a new one. But now I have this problem that, when I leave my phone locked for some time and then look at it again, the display does not seem to work. But what I can see is, that it doesn't turn black but more of a really dark blue, which I can state from turning it off with the home & lock button, because it then turns fully black. After restarting it it would work again as long as I'm actively using it, but then leaving it locked, it would happen again. And when I'm on the phone again, I can see that by restarting it, I accidentally made screenshots of the lockscreen, meaning that it must've been on, but I couldn't see anything.

Could it be that this is a problem caused by any damage when it was dropped, that something inside of the phone was broken as well? Or could it also be the battery?

Thanks for every answer in advance!