Samsung Galaxy S4 broken screen ADB autharization
I had exact same issue on my LG Volt when screen was broken. So first thing for sure you need to have enabled is "developer options" and USB debugging turned on.

Even when USB debugging is turned on when your computer will send encrypted digital key code for authentication you have to accept on your screen. 

That's for security purpose. 

There was one solution for enabling USB debugging but after that you have to confirm digital key code to access ADB shell... Etc...