With the TV staying on and only the picture is going out then the problem could be a couple of different things.
First, turn the TV on and make sure you can hear the sound. Shine a flashlight on the screen and see if you can see any image (you should be able to). If you can see the image then the problem is the backlight system. Most common the problem would be the backlight inside the LCD panel. Some time it is the power being supplied to the backlight, but when you have the picture to start with it tends to be the LCD portion not the power.
If the picture only goes out and the screen is a gray tint not black like the TV is off then the problem could be the main video processing board. This is an uncommon issue.
Most common problems like this are the backlight that is part of the LCD panel. Unfortunately, replacement LCD panels are not available for your model.