I am sorry that we cannot give you a better answer. 3 years is old for lot of HP laptops. in my opinion.
You might do some changing out... different hard drive, different memory...
remove the keyboard, and replace the CPU cooling fan, replacing it with another for about $27...
Hire a tech to test every circuit... Test, by replacement, the inverter that rests behind the screen at the bottom of the monitor.
If non of those make a difference, replace the motherboard, if you can find one.
You might also complain to HP, as HP does sometimes offer you a free replacement, if a large number of certain laptops have failed for no good reason.
The most common failure in the HP laptops on which we work is heat failure caused by the CPU cooling system plugging up with lint and dust... the resulting heat destroys the CPU or the system board. The second most common failure is a sudden and unpredictable failure of the system board.
Good luck. When you figger it out, let us know how you got it to working.
But it has been a long time... since 2004 anyway, since HP last had really rugged, long lasting laptops, in my opinion. Still, it may be worth while to talk to them... but they won't discuss anything until their certified techs have thoroughly examined the laptop. If they do, and it still doesn't work, and is out of waranty, they will charge you $80 for the examination and analysis.