I have a HP Nx8220 laptop which I have just replaced motherboard. When I plug in its original LCD screen it switches off. But as soon as I unplug it it runs fine even if I plug in a external screen. Can anyone help please!

:-)

It sounds like a short somewhere along the connection to the lcd screen. It's shutting off because it's protecting itself from frying. Make sure no metal is exposed where it shouldn't be, etc...