When the screen is "black", is is solid and black, or do you see a faint image when you shine a flashlight through the Apple symbol from the back? If you see an image, the inverter cable is at fault, since it provides light to the screen and often gets crimped in the hinge. If there's an image, dark screen or not, the video cable is fine.
I'd also pop the back of the screen casing off and verify that the video connector is fully seated. Sometimes the motion of opening and closing the laptop tugs at the video cable and causes it to disconnect slightly (especially when the screen has been replaced in the past, and the video cable hasn't been properly taped down again).