Welcome to Android Central! Does it give any indication of turning on? If you can see the screen glow, or hear some sounds, but the screen stays black, then the screen has probably failed, and you'd have to look into replacing it. If absolutely nothing happens, then it's possible the battery failed (best case scenario), or something worse like the motherboard.
Before contacting a Samsung service center, make sure you try a different charging cable/plug. Also, make sure you press and hold the Power button for at least 15 seconds to see if that forces a power on.