iPad stuck in boot up loop. 4013 error after multiple restore attempts
This may just apply to me, but I resolved this exact situation on my iPhone 5 by:


Replacing the screen on my iPhone 5 - I knew it had a faulty screen 


It would them boot into the "plug phone into iTunes" screen. Each attempt to resolving using iTunes on Windows 10 resulted in the Error 4013.


I updated to OSX 10.11.3 (current version at the time) and the latest iTunes. It restored the phone successfully, and resolved the Error 4013 issue.