Assuming that only the screen is broken, that your device thinks everything is ok and boots up and runs normally you might be able to remotely decrypt the card or access the data, but I think it's a long shot. First, the phone would have to be rooted. Then you would have to connect it to your computer and run a remote access program like Telnet or SSH. Unfortunately, I don't know of any way to do this without enabling or configuring the client device first.
From what I've read, the S4 doesn't use any hardware encryption so you should be able to reproduce the phone inside a VM running on a PC. You would need to obtain the exact ROM your S4 uses, load it into an Android emulator (try Virtual Box) then configure the ROM with your phone's unique (ESN/IMEI, etc.). There's no guarantee this will work as I haven't come across any information on what algorithm the S4 uses for encryption or how it builds the key, but I don't think there's any other way besides fixing the screen.