Ok, so I spent over 2 hours trying to fix this problem and I ran across this page in my search. Since I didn't find any solution on this page, I'll add my story to at least help out any stranger that crosses this This problem happened to me and my girlfriend, and this fixed both of our problems.
Obviously, check to see that airplane mode is turned off. Then make sure mobile data is turned on under More networks.
I initially had to switch over to the 3G network . This at least told me the phone was working. ( If you do this step and the phone still isn't getting data, i'm don't think this will help). Anyway, go in the settings menu by clicking More networks... Mobile Networks... Network Mode.and switching to CDMA. This on will cause your phone to reset. If your phone turns back on and has access to 3G, then I imagine this next step will work.
So, to fix this, I updated everything in the setting under More... System Update,(PRL, Profile, Samsung Software, and Firmware) and then I reset my phone.and wholla 4G was back on.
Hope this helps.