These things are very picky as to which LCDs they will use. The picture you put up is a G5 but the question says it is a Core 2 Duo. Look on the bottom of the stand for the correct one.
Next, there's a possibility that this old machine is one that has a screen recall on it. Go to Applications > Utilities > Grab application and take a picture of the whole screen. Now move that picture around using your mouse and determine it the lines are present in the picture or just on the screen.