This might sound like a stupid question as well, but have you tried holding the power button down for a long time? Sometimes my phone waits almost ten seconds while holding the button down.
The other question might be does the power button feel like its clicking when you press it in? sometimes the plastic button can slide off the mechanism a little bit. I had some dust get in mine, and it caused it to not always press in all the way. After I blew the dust out of the power button it hasn't happened again to me in over a month.