Hi people,
THE SOLUTION THAT WORKED FOR ME: CONNECT YOUR IPAD TO YOUR COMPUTER AND UPDATE THE IOS TO 8.1.2 VIA ITUNES.
Shortly after updating my non-3G iPad 2 to IOS 8.1.1 which I had to do in order to use the newest version of an application that was important to me, I experienced a complete failure to connect to wi-fi. It would attempt to log on to wifi routers but would grind away and was never able to complete the connection. I also noticed a "no service" indicator in the upper left-hand corner of the screen. Also, I kept getting the inexplicable message "unable to connect to cellular" which was especially odd because this is an non-cellular iPad.
I fiddled with some of the settings for a while to no avail and then I reset the "network settings" but this did not change anything. I was traveling at the time so I did not want to reset the whole system... that is a last resort and would cause alot of [unnecessary] work getting things back to normal.
When I got home I USB'd the iPad to my Macbook and iTunes told me the IOS 8.1.2 update was available. Halleluja! Strangely, the only fix in this update that was mentioned was some unrelated thing about ringtones. But this was my best shot and I commenced the update. I carefully watched it download and install and noticed there was a firmware update that ran during the installation. I thought this was a good sign. When it was done, my iPad automatically rebooted all my connectivity problems and weirdness were gone. Everything was back to normal, thank goodness. Apparently the secret firmware update had fixed everything.