Sounds like that switch might be faulty. If you have a multimeter with a continuity tester, (or a battery and a light globe) test to see whether it is able to break the circuit (no electrical connection) when the button is not pushed in.
If its broken, I suppose it'd be worthy of a warranty claim. Alternatively you could buy and install a small momentary push-button switch to replace it. Should only cost a dollar to buy from a radioshack (or other electronics store where you live) to replace the power button.