I am assuming you backed up you Mini to a Windows Computer with iTunes. If that is wrong, my thoughts do not apply
Sounds to me like your firmware on the iPad and the version of iTunes on your computer do not match – maybe you updated one side but not both at some point in time. If that is true, my guess is you are out of luck.
You certainly can restore the device (A much better word here would be RESET - not restore - edit by gwpotter) - which will give you an iPad like it came from the store, except the iOS version will be a newer version.
If you purchased music, podcasts, or software through the Apple Store, all that stuff can be downloaded again at no cost.
This kind of sitution can be avoided if you backup your iOS devices (Both iPhones and iPads) to iCloud, not a computer. If you have an iPhone you should think about this issue before you need to recover, store the iPhone or purchase a new iPhone.