What are you expecting the button to do?
A quick press switches the screen off (but music will continue to play & some apps may continue to run).
A long press (approx 3 seconds) will display the red "slide to power off" slider.
A quick press will wake it up (same as a quick press on the home button).
You'll need to hold it depressed for an extended period (3 seconds I think) to wake it up (the apple logo will be displayed whilst it's booting).