On my HP laptop, Fn and F4 toggles screen mode. If you're in laptop LCD mode an external monitor will go to sleep mode as there's no signal being sent to the monitor. Try plugging in the external monitor again, booting and hitting Fn and F4, or whichever is the screen toggle F button on your machine.
If the screen still shows an image, the issue is with the back lighting. Remove the screen bezel and check it out. If no cables are loose, you should be able to pick a complete screen unit or entire laptop with, say, a smashed LCD or liquid damage for next to nothing to swap an inverter out from.
Probably best not to bother with HP for spares. My NC4010 broke a 50 pence LCD hinge. Only way HP could supply a replacement was in a pair... attached to a screen! Found a pair of hinges in the end. Pricey for what they are at £15 but better than £300 for the complete LCD.
Good luck.