Hi @indigoee ,
What OS is installed?
Has the laptop been dropped or gotten wet at all?
Have you tried starting the laptop in 'safe mode' just to eliminate the possibility of a driver problem?
If you have and it is still no good try the following:
Turn on the laptop and verify that there is a normal display on the external monitor.
Then try shining a torch at an angle close the the laptop screen and check if you can detect the same image as on the external monitor. It will be very dim, so try this in a darkened room as it may help.
If you cannot detect an image at all then there is a problem between the GPU and the video cable connector on the motherboard ( or video cable to the LCD screen if you didn't replace it). Check that the video cable is securely connected to the motherboard.
If it all seems OK and you've tried a new video cable, then you have a motherboard problem.
If you can detect an image then you have a backlight problem.
As you have already replaced the LCD screen then the problem is either the video flex cable bewtween the motherboard and the LCD screen (don't know your laptop but if there is only one cable between the two then the backlight power supply cable is incorporated into the video cable), the backlight power cable connector on the motherboard, (if separate from the video connector) the backlight power supply (it may be fused with an onboard fuse that has blown) or perhaps the lid switch, (the lid switch is usually a magnetically operated switch (magnet in the lid below the screen) which operates when the lid is closed and sends a signal to the BIOS to turn off the backlight power) I'm not 100% sure re your laptop but I think that the switch is in the power button board.
Here is a link to the service manual for your laptop which may be of some help, although since you've already replaced the screen you probably won't need this.