Tap Settings > iCloud on your iOS device. Scroll down and tap Sign Out, then tap Sign Out to confirm. If you're using iOS 7 or earlier, tap Delete Account, then tap Delete to confirm. Tap Keep on My [Device] or Delete from My [Device], and enter the password for your Apple ID. Your data remains in iCloud, and is updated on your device when you sign in to iCloud again. If you're signed in on more than one device with this Apple ID, repeat steps 1-3 on each device. Go to your Apple ID account page, and sign in again. Change your Apple ID to the email address that you want to use. You'll need to verify the email address. Tap Settings > iCloud on your iOS device, and sign in with your new Apple ID.
I had this happen once or twice. If I remember right, I didn't have the hard drive ribbon cable seated quite correctly. Opened it back up, reseated it and was good to go. That's when I learned to not close it all back up until I had it all working.
You could also try Floola. http://www.floola.com/home/ , which is a standalone application that does not need installation and run under Linux (any GTK2 distro), Mac OS X (10.4 or newer!) and Windows (98 or newer, including Windows 7).