I have a Moto G 4G (with Lollipop) with the following problem. As soon as the boot sequence completes the screen turns black. It is not broken because the boot animation is shown, and I can take screenshots by pressing the power button and VOL DOWN. I can also see the screenshot animation (a white square that shrinks on the screen) and hear the shutter sound. By holding the power button the "Shut down" dialog appears and it can be touched, resulting in the phone shutting down.
I have tried running the phone in Safe Mode. Nothing changes (except from the Safe mode text in the lower left corner). I have also tried wiping the cache from the recovery twice to no avail.
Can you help me diagnose the problem? Or at least, is there a way to backup the data from the phone before attempting an hard reset? Please notice that the phone is locked, unrooted and the usb debug is not active, so I can't use ADB.