Introduction
This is the fix for Macs that boot to a black screen but still have the cursor visible. This issue seems to intermittently occur when a Mac, running Mavericks (10.9), installs a software update that requires a restart. People have mentioned that they've come in to find their Mac like this in the morning after leaving it on overnight, which would make sense as software updates install/reboot automatically.
Power the Mac down
Hold the power button for 10~ seconds until the Mac powers off.
Boot to Single User mode
Hold "command (⌘) + S" while powering on the Mac until you see a black screen with white text, at which point you can release the keys.
Wait for the command prompt ( :/ root# ) before moving to the next step.
Run a disk check
Paying attention to spaces, type:
/sbin/fsck -fy
Mount the file system as writeable
Paying attention to spaces, type:
/sbin/mount -uw /
Remove three files
Type these three commands, paying close attention to spacing, and hit return after each line:
rm /Library/Preferences/com.apple.loginwindow.plistÂ
rm /Library/Preferences/loginwindow.plistÂ
rm /private/var/db/.AppleUpgrade
The second one might return an error, it's ok if it doesn't find that file. Only a couple of the Macs I've encountered have required this to be removed as well
Reboot
Type this and hit return:
reboot
Re-configure the login window
While this process DOES fix the issue at hand it also reverts the login window back to it's default state. Login as an admin, navigate to System Preference > Users & Groups > Login options and set the options to look like the attached image. Restart the Mac once you're finished.
Credits to https://community.spiceworks.com/how_to/82502-mac-mac-boots-to-a-black-screen-with-cursor
Other method
If you happen to have logmein installed on the computer and a LogMeIn Ignition account on your mobile you can use the file access feature to remove the three files listed above heading "Remove Three Files" don't worry if the last file is not there. After you have removed them just forcefully power off the computer and start it back up and walla!