Wi-Fi won't turn on iPhone 4S? - 3

After my phone died one night my Wi-Fi setting to turn on turned light grey. It won't give me the option to even turn it on. I've tried resetting it (holding down the lock and home button until it restarts), I've tried just turning the phone off and back on, I've even tried connecting it to the computer but it won't back anything up therefore I really don't want to restore to factory settings.

Any ideas on how to make it able to turn on?

Added (1). Tried restoring network settings, still stayed light grey and won't give me the option to turn it on.

Added (2). Okay so I restored my phone to factory setting and it still won't give me the option to turn on Wi-Fi. I know that my house has Wi-Fi my laptop and xbox are currently on and connected to the Wi-Fi. I talked to apple support and they won't help me other then telling me to restore it.

Added (3). Interesting fact, iMessages are sending?

Added (4). Interesting fact, iMessages are sending?

LOVE is Beauty and Beauty is LOVE

Reset the network settings: Setting > General > Reset > Reset network settings.

Note that this will erase all remembered Wi-Fi passwords and Bluetooth pairings.

Edit: Have you installed the latest version of iOS? It's version 6.1.3 for the 4s.
If the iPhone is still under warranty, or if you have AppleCare, you can get a replacement. Otherwise, there's nothing you can do, unless updating fixes the problem.
iMessages can send over the cellular data network.