iPhone 5c keeps shutting down during power on
I have recently had problems with my iphone 5c with the battery running down low very quickly. I had my battery switched over twice, the first time was with a battery out my old iphone this battery did not work with my new phone. we then put the original iphone battery back into the phone and it turned on no problem, although it would no longer charge, the charging symbol came up and my phone wasn't running out but it wasn't charging either. The next day when I tried to turn my phone on it booted up then switched itself down 4 times before then turning on (it then ran out straight away). When my new battery arrived and we put it in the phone booted up then shut down again before it had chance to boot up fully. This is all my phone will do now. What can I do to fix this?