Try this
First, do the following:
Quit iTunes. Open terminal & type the following command or copy & paste:
defaults write com.apple.iTunes DeviceBackupsDisabled -bool false
defaults write com.apple.iTunes AutomaticDeviceBackupsDisabled -bool false
Press enter.
Once done, launch Disk Utility(from your Utility's Folder) , select your hard drive & then select "Repair Permissions". Once complete, launch iTunes, manually create a backup & see if that backup is now listed under Preferences>Devices.
You want to run permissions repair until the last line state: "Permissions Repair Complete", this can take 10~15 minutes or so. So, go back & run it until complete.
If this doesn't fix things(and, unfortunately it's starting to look like it won't), then only other thing left is to completely uninstall iTunes & then re-install. iTunes must be uninstalled in a certain order, so follow the directions here exactly. But, run permissions repair first.