Unplug the power, remove the battery and then hold the power button for 30 to 60 seconds. The DVD drive would spin up and attempt to read a disc if one was in the tray but still would not boot.
The HDD would spin up but the HDD indicator would not come on and would not boot. On power on the screen would stay black, no POST, nothing at all on the display. I had the same problem with my HP DV6599.