Start with the hardware.
Test cameras by taking pics as well as videos on both cameras. Plus flash, check that led works.
Conduct a voice call, see if you can hear as well as be heard clearly, use speaker phone too, and Bluetooth
Insert a readable sd card, see if it's read and see if can write.
Gps. Make sure you get a good lock on your location. Although this can improve with software updates, it should at least work out of box. Use google's turn by turn navigation, see that it is smooth, knows where you are as you're moving with car/bus etc.
Wifi. Try to connect to a router you know works.
Check all the Sammy gesture stuff. Make sure the sensors are registering your input.
Touch screen. Download an app that registers touch input on screen, that can show to you screen all parts of screen are active, some can show pressure of fingers too
Hook up device to pc, see if gets detected. Be sure to use a cable that provides sync capabilities and not just charges.
If you run into a problem with hardware, you know you can't really solve that one on your own, though you know software will usually improve over time.
I don't have S4 but jope that helps as a start.
Welcome to Android.
Posted via Android Central App