I have similar recent problem with my somewhat aged Centrino Lifebook C1110. Suddenly, the power on button will not start the Laptop, turning off almost immediately. By continually pressing this quickly it then starts (finally) and operates OK, until of course I power off and the same problem arisies but intermittently. Like others, I have depressed some areas of the keyboard surround and maybe this has the desired effect.
To take a look at the button, is it easy enough to simply lift the keyboard section and look underneath?
Thanks