A couple of weeks ago my daughter's iPhone 4 stopped charging from any source then went into a reboot loop. I put it into DFU then experienced the same 'error 14' message.
I established that it wasn't a USB bus/cable problem. My next step was to remove the battery (last known charge around 6%, so I guessed it was running on fumes after spending half an hour cycling through reboots) and replace it with another I had to hand.
This solved the problem and allowed me to restore. I subsequently swapped batteries again and the iPhone charged up normally. What I don't know is whether simply disconnecting and reconnecting the battery would have achieved the same result.
You don't mention the model of iPhone (or it's warranty status!) but my suggestion would be...
a) leave it plugged into an outlet overnight using your most trusted plug/cable combo, then try the restore again and if that doesn't work...
b) disconnect/reconnect the battery and try again
Feel free to skip to 'b' if you've got the tools to hand...
EDIT: not updated to reflect further info