My laptop turn on but display isn't working

It seems that it's not a motherboard issue.

If you can find a display replacement, that's my best guess.

First thing I would do is check the laptop on an external display over HDMI - as long as the keyboard caps isn't blinking, the machine is at least starting up. You can use a TV or monitor with the right cabling - even a CRT. It doesn't matter as it's a function test. Also check for an image with a flashlight as you may need it as if the display works well enough, Windows 10 and 11 favor the internal LCD when possible - Fn+F1 should override it, but look for the key with two displays. Also make sure the brightness isn't zero. HP typically has a minimum floor the backlight will always run at, so a fully black display could be hardware. This is the minimum floor on my EliteBook at least, yours is probably the same:

If the machine has a POST blink code on the keyboard, follow this to see what it is: HP Notebook PCs - Computer beeps or a light blinks during startup. There's a chance you can recover the PC by pulling the primary and CMOS battery and holding the power button for ~30 seconds