SIMPLE.
I had a similar problem where my HP 5000 wouldnt switch on and the power lamp was on indicating the power cable/charger is okay.
What i did is that i unplugged the AC power cable from the laptop, i pressed the power button and held on to it then i plugged the power cable to the laptop while still holding down the power button and then i released it and voila! It switched on. The problem is now solved!
Good luck