Hi,
Did the replacement screen also came with a new ribbon cable that connects it to the motherboard? If it does but will still not work but the external monitor does work the problem may lie in the GPU itself not the LCD that has been replaced.
I would suggest replacing the new LCD first that you got because if that will not work as well then the problem is the graphics card already and if it's soldered in the motherboard you'll have to replace the entire motherboard.