A) Post THE Product Number on the bottom of the laptop. It's in the white Service Tag. P/N = Product Number.
B) On the left/bottom side of the LCD screen frame (Display Bezel), there is a switch. Looks like a small button.
This is the Internal Display Switch. (May not be in this exact position for your model. Look around on the Display Bezel, that surrounds the LCD screen)
When the laptop is closed, the switch turns off the display, (Image on screen), with the computer still on.
Tap it a couple of times lightly, with the eraser on the end of a number 2 pencil.
See if anything happens. That switch may be bad.
C) Laptop off, monitor off, connect a VGA monitor to the VGA port on the laptop.
Example of a VGA cable, and VGA connector, (Port),http://en.wikipedia.org/wiki/VGA_connector
You can use a CRT monitor, (Looks like a small TV), or a flat LCD screen monitor if it has a VGA cable.
C) Turn the monitor on. If a CRT type of monitor allow it to warm up.
Turn the laptop on.
By factory default settings, the display should show on the external VGA monitor.
There are at least 3 display options,
1) Internal monitor of laptop ONLY
2) Internal monitor AND external VGA monitor
3) External VGA monitor ONLY
Press, and hold down on the Fn key. At the same time tap once on the Display Toggle-Over key.
Don't know what exact HP laptop you have. For most HP's it is the F2 key, or the F4 key, that is the Display Toggle-Over key.
(Key has an empty rectangle on it, with a vertical line on each side)
Still no display on the external VGA monitor?
Hold the Fn key down again. (Bottom left of Keyboard)
Tap once more on the Display Toggle-Over key
NO display on the external VGA monitor, means you have a bad graphics chipset.
(By using an external VGA monitor, you are bypassing the Internal Display Switch, and the Display Assembly. (Internal monitor of laptop)
If you have a display on the external VGA monitor, you have a problem with;
1) Video Cable, (Display Panel Cable for HP)
2) Display Assembly
Post back with your results, and if you have a display on the external VGA monitor, we will go on.
If you do not have a display on the external VGA monitor, you are looking at motherboard replacement.
Post back in a Comment.