Hi, it could be the cable that connects to the logic board and the LCD screen, but if the full assembly already included this cable then:" have you try to reset the PRAM and SMC"?. You can see the desktop ok in an external monitor so it is not the graphics card(controller), i have not notice that apple MacBook pro's have an inverter like PC's. in a PC if the inverter is bad then you will have those problems even with a new LCD screen.
Also there could be a small chance that even if the replacement is "new" that might be defective.