Why isn't my phone turning back on?

My IPhone 5s was working and then it wouldn't work anymore. i had replaced the battery because this has happened before. But I thought it was fixed, then it happens again. Some suggestions have been that it could be the lightning connector but im not sure what it could be. Back when it would go black and would be unresponsive I would take it apart and disconnect the battery and connect it back, and then it would work. But then it just wouldn't work. I tried disconnected it again, and now nothing. I have important things on this phone and need help. Any suggestions on what to replace now?