You can go through the steps of changing your battery and your lightning charge port. If that helps good. But like many 5c owners the u2 ic goes bad triggering these issues. I have read it's due in part to a 3rd party sync cable. Which is odd in my case I always use the original cables but my 5c will not charge any more nor will it come on. If this is your case and you are still under warranty with apple go immediately and try to exchange it. Like so many whom are not under warranty are out of luck unless you know some whom can micro solder to replace that chip.