This model uses LED's for the backlight and the power is supplied via a ribbon cable from the logic board.
Review this IFIXIT guide: [guide|27840|iMac Intel 21.5" EMC 2805 Display Replacement]. Jump to Step 20. Make sure the cable is correctly inserted.
Use a magnifier to inspect the pins of the cable and the socket as they could be damaged. If they look OK, you'll need to do a detailed inspection of the logic board as something has likely blown.