If DFU mode fails to work, here is the more tedious resolution -
Error 4013 is due to security software issues. Uninstall all security software completely, try again, if the issue persists I would either recommend another computer or calling AppleCare tech support at 1-800-APL-CARE (for US customers).
Note- this is even if your device worked fine prior to iOS 7 update with your security software. The change in the operating system on the device can cause compatibility issues with these other programs.
I hope this helps it worked for me!