A word of warning. The latest bootloaders in if installed prevent you from rooting, and at the time of typing there is no way around this. Do not accept any OTA upgrades if you want to root.
We need to know what type of SGS4 you have to help you,see here : http://androidforums.com/samsung-galaxy-s4/760098-18-galaxy-s4-models-know-yours.html
Please type in *#1234# from your dialler,and post back exactly what information you get. You should have three lines :
AP, CP and CSC.