Hook it up to an external monitor and see if the problem persists. This does sound like a damaged cable, now which one. When it goes black, see if you can still see the desktop dimly. We also need to know your exact model so we can direct you to the correct parts. Please give the last three letters of your serial number.
UPDATE Here's how to replace the display data cable: MacBook Core 2 Duo Display Data Cable Replacement
Here's the cable: MacBook Display Data Cable