Wi-Fi is grayed out and will not turn on. What can I do?

I would back up your iPhone and then restore the iOS and set it up like new to make sure it doesn't resolve itself http://support.apple.com/kb/ht1414 But other than that, if it continues, you may need some hardware service. There are a few places out there that aren't Apple that may be able to help, but if you are still in warranty or just like knowing its going to be fixed, I would call Apple or go to http://selfsolve.apple.com to set up service.