2013 iMac Update to Sierra with Black Screen Problem. I too had tried all the options of rebooting multiple times, restarting in safe mode, holding the shift key to prevent start up applications from running during login, and starting up in the recovery mode and using the disk utility to run diagnostics on my start up disk. All to no avail. I was reluctant to try to re-download the operating system or to back up from time capsule.
I tried the above mentioned trick and it worked perfectly: I turn my machine off, and restarted my iMac. Once the machine rebooted and the cursor was in the upper left corner with a black screen, I let the notifications appear on the screen and then one by one they disappeared as they had before. I let the machine sit for another 1 to 2 minutes to allow any other operations to complete.
At this point, with the cursor still in the upper left corner I typed in my login password, and hit enter and the screen reappeared as usual with all the background images, control bar, and folders appearing as normal.
I have not tried to reboot the machine or to reload any updates or operating system at this point for fear of any problems since I have some urgent work to complete. However, at this time everything seems to be working perfectly.
Good luck and thanks for the advice above.