ios 8.1.2 update error 16

hi, new to this forum, need assistance i sold my old iphone to a co-worker in work a month ago, it is just out of warranty he planned to give the phone to his daughter christmas eve, to cut a long story short, he plugged it into itunes and clicked update to ios 8 8.1.2 and the battery was it the red from what i understand the phone shut off(error code 4005) half way into the update and the apple logo repeatedly flashed so i put it into dfu mode and recovery mode and tried updating it no joy, swapped the battery with a new one and got it working, finally updated to ios8 8.1.2 thought it was ok but there was no signal only searching then i while later it came up awaiting activation, so i restored and put it into dfu mode and tried to update software again now error code 16 is coming up 3 quarters of the way into updating the firmware update have spent the guts of 30hours trying to fix the phone and have had no joy, have tried my mac running yosemite, windows 7 and windows xp and they all either pop up error code 4005 or 16 anybody care to shed some light on this, have researched this and seems alot of people have encountered this problem but no solutions as of yet