When I first started playing with NFC I seem to remember that the built-in apps didn't work. That may well have been my fault but I quickly gave up and started using the excellent NFC Task Launcher and Tasker with the Locale NFC plug-in. The latter is not for the faint of heart so I'd recommend starting with NFC Task Launcher. It's also free.
If NFC Task Launcher doesn't work, I'd wonder about the battery. The antenna is built into the battery. I bought two spare batteries for my S4 and despite otherwise looking and behaving exactly like the original battery, they appear not to have NFC antennae in them.