iPhone turns on and then back off

Hi I have an iPhone 6 which is driving me crazy.

The problem is that it will turn itself on, begin to load, and then turn itself off. Sometimes it can get as far as the welcome screen and other times it will not get any further than the apple logo.

I have tried restoring it from recovery mode and DFU mode. I have tried replacing the battery. None of these have worked. Is there anything else which can be done to fix the phone.

Any help is welcome!

Thanks