I have had the same problem since last android update. Start button not responding sometimes, in no particular case. Screen staying black and unable to use the phone for several hours. I had to reboot the phone until, for any reason, screen started to display again. Very very serious issue!
The issue occurred once or twice everyday, until : I uninstalled Facebook and deactivated Localisation. I don’t know which one has worked, but I’m relieved. The issue did not occured in 5 days (after one last reboot).
This might work for others.
Sadly, the problem did not occur during one month and then came back. Some days I can only access to my phone during 1hour. The rest of the day is spent trying to display anything/reboot/learning how to live without a phone. That is not what I expected from Fairphone