Hi
I'm no tech expert, so forgive my rudimentary grasp of the situation, but I've experienced this problem a lot since the Yosemite upgrade.
Perhaps my experience will help you or others with the same problem.
First, on my old iMac 27" (2009 model) although this was a white screen with cursor only, and now last week on my new 5k iMac (this time a black screen and cursor).
If I have the same problem as you, the iMac starts up, shows the Apple logo, and then the status bar begins animating to show that the system is booting up.
At about 30 percent, the status bar disappears, and the screen goes black.
After a lengthy call with Applecare, we seem to have solved the problem, and it was actually pretty simple.
Start the machine in safe mode (holding shift on start-up if you're new to all this).
iMac should start up properly, although will be a little glitchy.
At user screen, log in as usual, and let the desktop load.
Then open up System Preferences, and go to Users and Groups.
Click the lock and enter password to give permissions.
Under Login Items, try deleting all the items in the box.
Then click on Login Options (bottom of User window).
In Automatic Login - toggle to your specific username.
Click lock to save, and restart.
This SHOULD clear the error that was causing the issue.
I found that it helps to repeat the steps above and toggle again to switch Automatic Login back on.
I'm not entirely sure, but it seems that the additional functionality that was added recently around login options seems to have caused some sort of issue, where the machine can't decide whether to give you automatic access, or the option of guest user. This clash means the iMac simply opts not to offer any options at all. Hence the black screen.
Hope this helps. And thanks to Martin at Apple for patiently solving my problem.