Try shining a torch at an angle close to the screen to check if you can detect an image at all when the laptop is turned on. It will be very faint so perhaps try it in a darkened room as it might be easier to see if anything is there.
If you can see an image you've got a backlight problem. Since you say that the new screen and screen cable are OK it must be back on the motherboard.
I don't know how it works in your laptop but on a lot there is a magnet in the lid, below the screen that operates a magnetic switch in the case to turn off the backlight when the lid is closed.
On some, newer Asus models for one, the switch is incorporated on the same board that holds the Power button. It sends a signal to the BIOS to turn the backlight power on and off when the lid is opened/closed.
Not saying that this is the same in your laptop but check for any other cables connected to the motherboard around the Power button area perhaps which may be loose etc
I assume that the GPU still works because you say “…the unit is detecting the LCD because it shows in "Display Settings" when I plug into an HDMI monitor. “ and you’re getting a display on the external monitor OK. Is this correct?