Q: iPad Mini froze while updating to iOs 8.1

You might look at this ...

iOS: Not Responding or Does Not Turn On

http://support.apple.com/kb/ts3281

If you can't Update or Restore your iPhone, iPad or iPod Touch

http://support.apple.com/kb/HT1808

ALSO ... here are some other articles on Passcode and Activation Lock ...

iOS: Forgot Passcode or Device Disabled

http://support.apple.com/kb/ht1212

iOS Passcodes

http://support.apple.com/kb/ht4113

Find My iPhone, iPad, iPod a Touch or Mac

https://www.apple.com/support/icloud/find-my-device/

Find My iPhone Activation Lock

http://support.apple.com/kb/HT5818

Find My iPhone Activation Lock: Removing a Device from a Previous Owner's Account

http://support.apple.com/kb/ts4515

Apple release Tool to check the Activation Lock Status of iOS Devices

http://www.idownloadblog.com/2014/10/01/activation-lock-status-check/

I'll give you something else for the near future ... it's doing a clean system install and it's a good way to get rid of any possible corrupted files in your system. This can also be for troubleshooting a particularly difficult problem.

Follow this procedure for a Troubleshooting Methodology ... basically reset to factory default condition -BUT- be sure to do the following methodically and also to follow the part with Apple Support!

First you want to make sure you have several backups of your data and done with a couple of "different" sources. Be sure to understand what data is backed up and what is NOT on iCloud Backup and iTunes Backup. Use a variety of methods for backup ... you might check into Dropbox, in addition to your Apple options.

Then turn off your desktop anti-virus software when using iTunes for this reset to factory default. After you do that reset, then leave your iPad in its factory default state and see how it operates then. If you encounter any problems in that factory default state, then take it to Apple Support, and let them know that you have just reset it to that state with iTunes and have not put any of your data back on and it is operating in this fashion (whatever the problem is) in that pristine state. Make sure you keep that trouble ticket number, because if it has to be escalated through Apple Support, you're going to find all communications tied in with that number. If the lower level help isn't able to help you, then escalate it to a higher level to examine the problem. Keep at it with that trouble ticket number until Apple Support arrives at a solution to that problem. Be methodical and keep at it.

On the other hand, if everything is okay with the factory default condition, then restore your backup. Some people have discovered that the problem resides in the apps or something in the restored backup. If that's the case, then it's going to be trying and difficult to find out which developer's app is causing you the problem. And ... it's true ... that a developer not following Apple's instructions and guidelines for his app can CAUSE YOU TROUBLE. This kind of thing does happen from developers, especially when a new system upgrade comes out, because some developers ignore what Apple tells them about changes coming, and what they do BREAKS SOMETHING.

This is a troubleshooting methodology that you are going through. See it through to the end.

Choosing an iOS Backup Method (Should I Use iTunes or iCloud to back up ...)

https://support.apple.com/kb/HT5262

Back up and Restore your iOS Device with iCloud or iTunes

http://support.apple.com/kb/ht1766

iTunes: About iOS Backups

http://support.apple.com/kb/ht4946

Create and Delete iPhone, iPad and iPod Touch Backups in iTunes

http://support.apple.com/kb/ht4946

iOS: Troubleshooting Encrypted Backups

http://support.apple.com/kb/TS5162

Use iTunes to Restore your iOS Device to Factory Settings

http://support.apple.com/kb/ht1414