If the LEDs show activity when you power up and it appears to be booting, in my experience, I have found a number of HP LT that develop loose video connectors.
However, I would first do the flashlight test for backlight. Sometimes there are 2 connectors. A small one supplying the backlight and a larger one for the video.
You should be able to access these by removing the KBD. The look for cables going to the screen.