When you say "clicking sound" do you mean the sound the button makes when it's pushed, or the startup chime?
Sometimes the Powerbook will just take a few moments for the screen to register that it's starting up (go to the gray startup screen) even though it's been started for some amount of time. So, push the power button and just wait 10 seconds and everything should be good to go.
If, on the other hand, you pushed the power button, waited some amount of time, and the PB didn't start up (repeatedly), then it may be a bum switch and I'd have it checked out. Another way to check is to see if once the PB has started up, if you push the power button, does it quickly (and always) go to the "Sleep, Restart, Shutdown" dialog? If it does, then the switch would appear to be working and there may be another issue.
I'm assuming, of course, that there aren't other issues (not plugged in, bad battery, etc.).