I had my nexus 6 in the same state. Reboot to fastboot mode (power + vol down), connect the phone to your PC/Mac via USAB and get the Android "fastboot" executable on the PC/Mac. From here, try a "fastboot format cache" + "fastboot format userdata" then try a fastboot reboot. Worked for me. Of course, you loose your data, but you save your phone :-)