Several Nexus S owners, myself included, start to experience this problem with the phone after a year or so of using it. You can create a nandroid and try a different ROM to make sure that its not AOKP causing the problem, but most likely its a hardware failure. If your phone is still under warranty you can try sending it back otherwise you'll have to deal with it (I have the same problem and its a pretty big pain, because the phone turns on by itself. I'll probably be upgrading in the fall though). You can remap the search key as the power button with an app called "button remapper". Its not in the Play Store but its on XDA.
This app on the Play Store lets you create a widget to turn of the screen. With Android 4.0+ you can turn on the screen by using the volume buttons by navigating to Settings > Security and then setting lock screen to none. ROMs such as CM9/CM10 and AOKP ICS (not sure if this feature is incorporated into AOKP JB yet) let you turn on the screen with the volume buttons with out disabling the lock screen and CM has a toggle in the notification bar that you can set to turn off the screen. The biggest problem for me is the screen turning on when the phone is in my pocket because the power button is loose. Its a pain, but hopefully this will help
More links:
http://productforums.google.com/forum/#!topic/mobile/rkbvoQ0tf-k
http://www.youtube.com/watch?v=snyfboC0AJY
