Q: error 4013 Help please

Run Console for any further details.

For advanced solution try to Download and install OS X USB Debug Kits which will provide more information about USB device and interface detection, driver and interface matching, driver loading and information generated as a result of normal and abnormal conditions.

I have the same error. 2 weeks before the end of contract as well. But that time has now lasped. I've tried reinstalling Itunes, rebooting DNF mode (is that the correct term), different cables, laptops, ports, removing all security software. Will the above software work? Usual find these extra programmes writen by others don't usually help. Would apple recommend  that?

Can anyone else suggest anything else? Emailed apple, no reply yet. Please help, its frustrating as I need to use the old one.

Planned Obsolescence?? 

Tried that with three different computers. Will I be able to try in a apple store? Not one locally though. Old network provider wouldn't help.

Btw still no reply from my email to Apple.

I know it will sound very weird but it worked for me,I put my iPhone5s in a zipperbag and put it in a deep freezer for about 20-30mints, after that I tried restoring it and it worked very well, now its restored and working fine.

if nothing works you can try this out. All the best.