The apn is what you need for data to work.
Go to settings > connections > more networks > mobile networks > access point names. You should see an apn for AT&T. If you don't you will need to add it. I have the T-Mobile S4 so I'm not sure what the settings would be for AT&T.
I found these for the AT&T S4. You can see if they work if you don't have it. Press your menu button and select New APN.
Name: ATT Phone
Proxy: Not set
Port : Not set
User name: Not set
Password: Not set
Server: Not set
MMS proxy: proxy.mobile.att.net
MMS port: 80
Authentication type: None
APN type: default,mms,supl,hipri
APN protocol: IPv4
APN roaming protocol: IPv4
Enable/disable APN: APN enabled