My 2 1/2 year old HP Pavilion DM4 running Windows 7 failed to start from sleep. The behavior was two audible clicks about 3/4 of a second apart, the power light on the cover would come on during the 3/4 second interval, and that sequence would repeat every 5 seconds. By putting my ear close to the exhaust vents I could hear the faint sound of a motor starting up during the 3/4 second period, but stopping at the end of that brief period. The power button had no effect whatsoever.
Googling for a solution for a non-starting laptop I found a recommendation to discharge electrostatic electricity from the laptop. Unfortunately that procedure required removing the battery which I was unable to do because the button on the cover securing the battery was broken.
Since the laptop was powering-up momentarily every few seconds using-up battery power, I decided to unplug the power cord and let the battery discharge. After about 48 hours I found the laptop completely dead, and pressing the power button had no effect.
I plugged-in the power cord, waited a few seconds, pressed the power button, and Voila!, working laptop. I restarted the machine, put it to sleep, put it in hibernation. Operation resumed normally afterwards in every case.