Hi All,
I just resolved my 3014 problem which all started with my iPad mini 32GB iOS 6 to iOS 7.1.1.
At first I thought it had something to do with the available diskspace on the computer C: drive. So I made sure to housekeep all temp and interent temporary files. Empty the recycle bin to increase diskspace from 6.6 GB to 7.34 GB. I had a problem in the past where diskspace was chewed up big time by iTunes iOS devices' *multiple* backups - today iTunes only keeps a single backup for each distinct iOS device.
That did not work as expected but it did jogged my thinking cap and memory that perhaps the Apple ID which I had logged in had something to do with it. See, I had registered the iPad mini with Apple ID (A) and iTunes was logged with Apple ID (B). I merely ensure I logged out of Apple ID (B) and verified that Apple ID (A) was indeed the current Apple ID logged into iTunes.
Wah lah, the so called unknown error 3014 did not appear on the first attempt to perform iPad recovery after the latter method (above paragraph) was done.
Hope the rest of our iPad brothers and sisters having 3014 problem will find that distinct method to resolve this pain in the arse problem. Mine was just trial and error and not taken from any internet forum - I hope my entry here can be of help to those who have multiple Apple IDs on the same computer.
Best of luck people.