Its hard to say what the problem might be. Did you just update to iOS 6.0.1? Anything that you can correlate the issue with? Something that you just downloaded or did you just restore the iPad and the problem arose?
Have you tried restoring from a backup - if the WiFi setting was working before?
This is copied from Appletoolbox.com about dealing with the greyed out Wii issue.
Apple's support article for this issue.
Some things to try first:
1. Turn Off your iPad. Then turn Off (disconnect power cord for 30 seconds or longer) the wireless router & then back On. Now boot your iPad. Hopefully it will see the WiFi.
2. Go to Settings>Wi-Fi and turn Off. Then while at Settings>Wi-Fi, turn back On and chose a Network.
3. Change the channel on your wireless router (Auto or Channel 6 is best). Instructions at http://macintoshhowto.com/advanced/how-to-get-a-good-range-on-your-wireless-netw ork.html
4. Go into your router security settings and change from WEP to WPA with AES.
5. Renew IP Address: (especially if you are droping internet connection)
• Launch Settings app
• Tap on Wi-Fi
• Tap on the blue arrow of the Wi-Fi network that you connect to from the list
• In the window that opens, tap on the Renew Lease button
iOS 6 Wifi Problems/Fixes
Fix For iOS 6 WiFi Problems?
Did iOS 6 Screw Your Wi-Fi? Here’s How to Fix It
How To Fix Wi-Fi Connectivity Issue After Upgrading To iOS 6
iOS 6 iPad 3 wi-fi "connection fix" for netgear router
Apple's iOS 6 Wi-Fi problems
Look at iOS Troubleshooting Wi-Fi networks and connections http://support.apple.com/kb/TS1398
iPad: Issues connecting to Wi-Fi networks http://support.apple.com/kb/ts3304
WiFi Connecting/Troubleshooting http://www.apple.com/support/ipad/wifi/
How to Fix: My iPad Won't Connect to WiFi
iOS: Connecting to the Internet http://support.apple.com/kb/HT1695
iOS: Recommended settings for Wi-Fi routers and access points http://support.apple.com/kb/HT4199
How to Quickly Fix iPad 3 Wi-Fi Reception Problems
iPad Wi-Fi Problems: Comprehensive List of Fixes
Fix iPad Wifi Connection and Signal Issues http://www.youtube.com/watch?v=uwWtIG5jUxE
Fix Slow WiFi Issue https://discussions.apple.com/thread/2398063?start=60&tstart=0
How To Fix iPhone, iPad, iPod Touch Wi-Fi Connectivity Issue http://tinyurl.com/7nvxbmz
Unable to Connect After iOS Update - saw this solution on another post.
Note - When troubleshooting wifi connection problems, don't hold your iPad by hand. There have been a few reports that holding the iPad by hand, seems to attenuate the wifi signal.
If any of the above solutions work, please post back what solved your problem. It will help others with the same problem.