Phone won't switch on

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.