Like a laptop screen, there is a video connection between the screen and the camcorder's main board, which is likely a small ribbon cable inside.
As the video output to a television is fine, it apperas to be problem with this internal video connection. Unfortunately, it does mean that the camcorder will need to be opened to physically check this cable.
One possibility is that the cable has come loose from its connector at one end. If this is the case, it is basically a matter of opening the connector's clip, pushing the ribbon cable in fully and closing the clip. However, if it's a broken wire on the cable or a bad solder joint on the connector, this will be more difficult to fix.
Unless you have experience with dismantling and reassembling small electronic items (excluding PCs ), I would strongly advise against taking apart the camcorder. Generally someone experienced in repairing electronic items (such as TVs, Hi-Fi systems, etc.) should be able to fix this.