Chosen Solution
I have an iphone 5s with a BLACK and unresponsive screen. Nothing shows on it and it does not respond to touch. This phone screen is 100% not cracked but loose in the metal case (yes it’s been dropped a million times - screen protected by screen saver - and lives in a back pocket of teen’s tight jeans) I can use quicktime to see/mirror the screen and the phone is charging and powered on. Is it just the screen?
Ben is right, this could be a simple case of a faulty screen. However, the best way to determine this is to plug it into a computer (when you know it’s on) and see if iTunes recognizes it is plugged in. If it does you know at least certain components on the motherboard are functional. A replacement screen could (and likely will) do the trick. However, it could also be an issue with the chips on the board themselves. That’s a more complicated repair…so let’s assume a faulty screen. Return the one you got, get a new one, and check for persistent issues.
I’d say, see if any local phone shops might check it out for little to no cost…