This article outlines how to determine if the backlight has went out on your Elo monitor. 

If your Elo monitor comes on for just a second and then goes back off showing nothing but a black screen, and the monitor is an older monitor, it could possibly be a problem with the backlight or backlight inverter inside the monitor.

Each monitor is equipped with a backlight to illuminate the screen. If this backlight or the power inverter that turns on the backlight goes bad or is in the process of going out, it will result in a black screen. This is a hardware failure and the monitor would need to be replaced or sent in for repair if still under warranty. If the monitor is more than 5-years old it most likely cannot be repaired due to lack of parts available and you would need to purchase a new monitor.

Often times when backlight failure occurs, you can use a flashlight to shine into the screen and faintly see video, however, most of the time it just appears to be a black screen.

For information on how LCD/LED backlighting works, see this Wiki article