When you say that the display turns off and on when you unplug it does it completely shut down or was it just the display and the laptop stays on? Here are some troubleshooting steps that may help.
- Start by doing a hard reboot, remove the battery and unplug the AC adapter then press and hold the power button for 20 seconds then try it again.
- If the problem will still persist the problem may lie on the built in display.
- Connect an external monitor and see if the same problem will happen with it.
- If it does that could only mean that the graphics card is faulty.
- If it doesn't happen on the external display that means the built in display is faulty.
- You can check if the ribbon cable is connected properly to the motherboard or to the LCD itself.
- if all these will not work unfortunately you'll need to replace the built in display.