The power button on my Galaxy Nexus stopped working
If the phone is working normally except for the power button not responding, you most likely have a hardware issue. That is, the power button is probably physically broken.

In this case, you will need to return the phone to the manufacturer or the point of purchase for a repair or replacement.

Before returning the phone, copy off any personal data you wish to keep, and remove the battery, SD card, SIM card and any external case; do not ship those or any other accessories back along with the phone. You may get a replacement phone, and your data and accessories will not be transferred.