iPhone 5s bootloop: red screen of death not fixed by camera/prox cable

My iPhone 5s recently starting going into a bootloop. It boots up with the Apple logo, then after a few seconds shows a solid red screen. It then goes back to the Apple logo, and the process repeats indefinitely.

I've seen other posts on here and elsewhere saying that disconnecting the camera/proximity sensor cable will fix the problem. In my case, it does not. The behavior is unchanged. I can't seem to get into DFU mode either. The phone bootloops in that case too, just without the red screen.

Also, this seems to happen to most people after a screen change, but in my case there was no screen change or any other type of fiddling inside the case.