As repair tech extraordinaire jessabethany has said: A phone that is vibrating with no display is telling you, "My display isn't working, my display isn't working!" This is how iPhone behaves when powered with a nonfunctional display.
If your phone has never been opened, the issue could be a simple software glitch. Perform a force restart and see if it resolves the problem.
Display cable(s) disconnected
Your iPhone screen's flex cable connectors may have popped free after a drop. Follow your iPhone's screen replacement guide to check each connection and re-seat it if necessary.
Display cable(s) damaged
If not, there could be damage to the display's flex cables—in particular, the LCD flex. Inspect the cables carefully for damage. Replacing the screen can solve the problem.
Cable connector sockets damaged
There may be damage to the LCD or digitizer flex cable socket on the logic board. Check the sockets for debris, bent pins, etc., and attempt to remedy the problem. If the socket is damaged, a skilled technician can replace it as a board-level repair.
Blown backlight circuit
You may have a blown backlight filter (like a fuse). (This can easily happen when using certain replacement screens that have an exposed backlight flex solder joint—pressing the screen into the frame will cause the exposed joints to short the LCD line to ground and burn the filter.) This can also be fixed as a board-level repair.
If none of the above applies, you may have drop damage or latent water damage that is causing a problem elsewhere in the backlight line. This will likely require more detailed troubleshooting and a board-level repair.
This behavior has been observed in:
- iPhone 4 (CDMA Verizon)
- iPhone 4S
- iPhone 5
- iPhone 5c