i've had this asus laptop for about a year and a half, and i've had a problem with the power button for a couple of months now. it takes a ridiculous amount of presses in order for the laptop to actually turn on; often, i'll have to sit and press the button continuously for 10-15 minutes to get it to work. also worth noting that the right quarter of the keyboard below the power button only occasionally works - this includes the keypad and the right arrow, but oddly not the page up and down buttons which are right next to the power button.
Try taking it apart, disconnecting the power cable that goes to the button, and manually shorting the pins. If that doesn't work, then it is probably a mobo issue and it will need to be replaced. The fact that part of the keyboard stops working reinforces my opinion that the mobo is the issue.
If shorting it does work, then you can just replace the power button.