Do this test to determine if its the back lamps or the display board - with the monitor powered on and the computer pushing an image, darken the room and take a flash light at a 45 degree angle to the screen - do you see an image? If so, the back lamp is shot which can be replaced.
If you still do not see an image with the flashlight the display board is often shot, which can also be replaced. With the low cost of LCD screens now they can be found pretty cheap.
I'll also add because of the related topic, if you have a Samsung LCD TV and it won't power on, you might be suffering from bad capacitors which the Samsung line has had an ongoing problem with. I've fixed about 20 TV's of various sizes and they all have failed due to the same problem - one or two bad caps on the display board. A bad cap can "usually" be identified by examining the top of the barrel to see if its raised. A bad cap doesn't always rise but a cap that has risen will almost certainly be bad. They are cheap and easy to replace.