Awesome. Hope everything goes well. Basically just "downgrade" to iTunes 11.0.5, and follow the Failsafe Restoring guide provided by Marilyn. I'll re-post the link below for your convenience
TUTORIAL - Failsafe method to restore the current version of IOS
Bring it to the Apple Store and have them check it out. If you're under warranty/AppleCare, you can either get it fixed or replaced. If not, you can still get a free diagnostic test ran to see what the issue is.
I'm pleased to report that I managed to get iOS 7 onto my iPad via a friend's computer.
Willerz2 and mickey330, thanks again for all your help!