|Image Source: iOS Recovery|
I ended up on an article called "iPad Recovery Mode: Fix a Locked or Stuck-at-Apple-Logo iPad" from the site About.com. I had never had to restart an iPad in Recovery Mode and was happy to see it wasn't as difficult as it may sound. Read through the articles if you find yourself in a similar situation, especially after updating to iOS 8 or the more recent iOS 8.1 as my principal did.
One thing to note, it is recommended to have your iPad connected to your computer, but you can also use the "Find My iPhone" app or use iCloud.com to do a remote wipe of the device. Not as fun of an option if you don't have a back-up, but you should be doing that regularly though, right?