anytime i do Samsungs i order by model number, for the most part screen, battery, cameras are the same, the charging ports is what i order specific based on model number unless you just solder the new port then it is the same.
You can buy the battery, pentalope screw driver, 000 screw driver, isasemo and a spudger from ifix it and use this guide How to Replace Your iPhone 6 Battery. you can remove the vibrator to get more clearance. just don't pull the tabs up towards the ceiling and away, you want to pull the tabs and keep pulling and be horizontal as possible like you are following the top part of the workspace. Please put back the same screw from the same hole it came out of. study the guide afew times before doing the repair and you will have a good running phone again.
@stingersys when looking at charge ports look behind the battery or on the charge port itself and find the model number. example Verizon will be like N910V. order what is on the device currently. hope this helps.
can you try a new or a friends S4 battery? If you plug in the charger and can see the battery charging or the battery logo it may be the power button. Galaxy S4 have a power button that will need to be soldered on in order to replace the Button. the only way to test the button is by opening it up and testing the button itself for continuity on the connectors. If the charging port is bad and not charging the battery it may not turn the phone on. try another charging cable also just to rule it out. hope this helps.