Could be a bad screen, if you shine a light on it, can you see anything? If so, your backlight needs to be replaced. If you can't see anything at all, try connecting an external monitor to it, with a keyboard/mouse, turn it on and quickly close the lid. If you get a display on the monitor, the LCD screen is bad. If you get nothing, could be the motherboard.
Did you try running it without the battery, just on wall power?