iPhone 5c Boot Loop problem

So it.s like this , iphone got an uppdate from itunes, but after than it entered into a boot loop.

The phone can be power on using the power on/off button ,but it can be turned off only using power on + home buton combo !

Phone powers on but right at apple logo, it stay there for 3 sec then the apple logo fades to grey (just like a broken lcd) then it restarts... and it does this on and on and on ... until the battery is empty.

The phone enters DFU mode , itunes recognized it, but after itunes kick the iphone from dfu mode , and itunes says "waiting for iphone", the phone restarts but instead of continuing the restore procedure , it enters the same loop ,and after 10 minutes itunes gives error .

The phone is out of warranty , and i want to save it just because it looks perfect, doesnt have any sign of usage !

Oh, and another thing i did try to put another Original apple battery (i hade in hand 6 brand new one !! ) didnt work ...

So guys i came to you for your opinion. Be free to say anything you think will fix this poor iphone !