How to recover an iPad from power-off during an upgrade? I upgraded my iPad 2 from iOS 6 to iOS 8.

However, I cancelled the upgrade by turning the iPad off because I thought that my files weren't backed up to a PC. I used OtA upgrade.

When I turn the iPad back on, there's an image of USB connector and iTunes icon signifying to connect it to iTunes.

Would all my files (photos, paid apps, memorable videos, etc.) still restore to my iPad if I restore from iTunes?
No - you would need to try to back up over USB to PhoneView or a similar tool.

Once you're sure you can't get any data back, then connecting to iTunes can easily wipe whatever's left and then return a proper working OS onto the hardware.