To see if it works on the Gateway I think you'll just have to try it. Dell's designs were such that you changed the entire top lid (that part with the LCD) and you could get a higher or lower resolution.
I have a Gateway FX P-7805u ( with the 1400 X 1200 resolution screen ) that has some issues with the case being cracked and the fans are going out. I recently bought another FX P-7805u (with the 1400 x 900 resolution screen).
They both have the same identical video card installed.
Is it possible to swap the higher resolution screen onto the other laptop? If so, what all would need to be swapped? CPU, etc…