Hi,
From your description it is not passing POST (Power On Self Test) or even trying to start POSTing.
To eliminate the possibility that it is a corrupted BIOS that is preventing a normal start try a power refresh and see if that resolves the problem
Disconnect the charger if connected and then open the laptop and disconnect the main battery from the motherboard (you don't have to remove it, just disconnect it). Next remove the RTC coin cell battery from the motherboard and then press and hold the Power On button for a ''full 30 seconds'' and then release it.
With the RTC battery out, measure its voltage. if it is <2.5V DC replace it. It is a RC2032 coin cell battery, available most everywhere e.g. supermarkets.
Reinsert the RTC battery (+ve on top), reconnect the battery, connect the charger and try turning the laptop on.
Not that you need it but here's the [http://h10032.www1.hp.com/ctg/Manual/c05357609.pdf|maintenance and service guide] for the laptop. See p.34 and p.55 to see how to disconnect the battery and remove the RTC battery.
If still no good, what is the make and model number of the motherboard as printed on the motherboard itself, e.g. DAG35???? perhaps? The schematic may have to be found to find out what's wrong.