Thankyou for the update, and thanks for explaining the company perspective. The steps for restoring an ipad can be found here
http://support.apple.com/kb/HT1414
Before starting any restore I would suggest you go to Settings\Safari and clear out your history, cookies, data etc. Turn debug off, java on, private browsing off (will cause problems loading pages like CNN because of cookies issues) set cookies to 'When visited'.
Open new tabs in background (when off it can hang pages with lots of media content)
And in Advanced settings - remove all website data.
Clear History and clear cookies and data - you need to have any backup as clean of any junk and clutter as possible
Prior to backup also disable Restrictions in Settings\General
Ensure you have a full charge on your pad before you start, as the restores will require connection by cable and any powering will be what is available through your usb which will be minor.
Depending on your configuration it can be a long process - so have a good book to read or something else to keep you occupied. Also be available to keep an eye on the process for any hangs, errors or issues whilst it restores.
Because you may have a settings issue with another App, my advice would be to perform a backup - but then unsync your Apps before commencing the restoring process. In this way the data in your Apps is preserved in the backup - but will only write back that data for which you have Apps installed when you restore from that back-up. The Apps themselves are not backed up as they are in your library.
Similarly, I would recommend going to Settings\General\Reset and Reset Network settings, also turn wifi and data carrier off in settings so your ipad cannot initiate another connection before you have finished. There is one other area known to be problematic with the iOS 5 variants - they all need to have the latest updates for the following installed if you use them. Itunes (obviously) and if so it will not hurt to run a repair routine on it prior to starting. Repairs and checks for the latest of the following will not go amiss either
Apple Application Support
Bonjour
Quicktime - (often overlooked)
Safari - especially if you sync bookmarks (iTunes - device connected, clicked to display summary page, select Info page and untick for this repair so that bookmark corruption is not an issue).
icloud Control Panel Applet
Apple Software update application
Then:
wifi/carrier off
Network settings reset
Backup
Unsync Apps
At this point - and as an after thought I wondered if you can go through your iTunes settings under the Edit Menu\Preferences - Parental for instance is not locked down with any hidden settings etc.
Whilst in the Advanced tab click on Reset warnings. Also:
Right click your device in the main iTunes window and select to Reset Warnings there to, this will allow previously ignored warnings to re show if they occur again.
Restore iOS - but dont elect to restore from your backup just yet - just restore to 5.1.1
When finshed switch back on and test wifi and safari.
If all ok, resync your Apps a few at a time to see if you can isolate a possible cause.
If the problem re-occurs before you reinstall any apps and reinstall their data from backup - it may well mean a possible hardware issue, and or a configuration file not as it should be (Plist - Property list) that is being utilised with the restore process.
Finally, a small apology
I know my answers seem a little long winded - but rather than just refer you to support articles I have tried to pool as many workarounds as possible into my replies, so that if you follow them through, I will know what you have done and what you have not. Hope you understand I am not just trying to wear your eyes out ;)
Kind regards
Nick