P.S. Explorer was running in my case. I could see my taskbar at the bottom of the screen but my desktop had no wallpaper (completely black) and no icons.
Except for the wallpaper factor that doesn't sound like the same symptom. That sounds just like your Display configuration (aka Project) is set to Extend and you are starting in Desktop (or you have Show Taskbar on all displays checked) but as I indicated somehow your main monitor is being used as your secondary. Press Win-P, CursorUp, Enter to change that case.
In fact, though, I suppose this same (hypothetical) quirk could explain others' blank screen symptoms. E.g. their default would be to start in the Start Screen but their Taskbar option would be to have it only on the main monitor (which they can't see or which would normally be hidden by the Start Screen.) But then with the new "MUF elements anywhere" change that occurred in W8.1 they should be able to see those MUF bars regardless of the monitor which was current, e.g. Win-C for the Charms bar, etc. Then again, maybe not being able to do that would be consistent with your lack of wallpaper symptom. E.g. another sign that explorer.exe is broken and needs to be restarted at least.
BTW others with a blank screen are claiming no keyboard workarounds are possible but do say they observe the Network icon (probably from the Lock screen) "flashing" on the left and then the screen can show mouse movement but no input of any kind is possible. Please say if that Network icon is appearing at all for your case(s). That would be a clue for how far things are progressing before the blockage.
FWIW I don't know what event log will be involved with this but I imagine that it would help to have some extra tracing enabled for whatever it is. For a guess try opening WindowsUIImmersive (under Applications and Services logs) and try enabling its Operational log (for a start). I'll turn that on too and see when it starts recording after a boot. I suppose results will also depend on your Navigation options regarding Start Screen. E.g. I have When I sign in or close all apps on a screen, go to the desktop instead of Start checked so possibly might not see any immediate tracing in there at all after a boot. TBD.
HTH
Robert