Is the screen fully black - or do you see any parts of the screen image (login screen, or menus and icons from your normal desktop) even if very dim. That's easier to see if you shine a bright light into the screen. If you do see dim icons or other images, then you likely have a failed backlight board.
If the screen is really completely black - no menus, nothing, then you could try reseating the video cable.
You can also try connecting an external monitor to your iMac, if you have that available. If you get good video on the external, then you may have a failed LCD panel.
There ARE some LED diagnostic lights inside that can help you decide what you can do.
You can find a service manual for your iMac online somewhere. You can search for the name of the pdf.
(If you have a 27-inch, you just replace the 21 with 27 to search for the correct manual.
That will show you how to get at the diagnostic LEDs, and how to interpret them.