Black screen with cursor issue

I came across this a while back for something similar to what you describe:

I had the same issue with my 2008 iMac and Apple support walked me through the fix yesterday...

1. Shut the computer down by holding the power button for 10 seconds

2. Restart the computer and press shift at the same time until you see the progress bar start moving

3. Once you reach the point where your screen goes dark and you see the cursor, type the first letter of the username for your computer, then hit Enter, then type your password, then hit Enter.

4. After a moment, you should see the spinning beach ball

5. Your screen should then move on to something along the lines of "Completing OSX Installation" (I can't remember the exact wording). Let it finish. After that it should go to your normal desktop and the issue should be fixed. (If your screen goes pitch black during this process, hit the space bar. I thought it wasn't working, but the screen was just sleeping).

Apparently it's an issue with an automatic update that never quite got past the login screen.

Try reinstalling OS X:

Reinstalling OS X Without Erasing the Drive

Boot to the Recovery HD: Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears.

Reinstalling OS X Without Erasing the Drive

Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the main menu. Repair the Hard Drive and Permissions as follows.

When the recovery menu appears select Disk Utility and press the Continue button. After Disk Utility loads select the indented Macintosh HD entry from the the left side list. Click on the First Aid tab, then click on the Repair Disk button. If Disk Utility reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit Disk Utility and return to the main menu.

Reinstall OS X: Select Reinstall OS X and click on the Continue button.

Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.

Alternatively, see:

Reinstall OS X Without Erasing the Drive

Choose the version you have installed now:

OS X Yosemite- Reinstall OS X

OS X Mavericks- Reinstall OS X

OS X Mountain Lion- Reinstall OS X

OS X Lion- Reinstall Mac OS X

Note: You will need an active Internet connection. I suggest using Ethernet

if possible because it is three times faster than wireless.

Startup Issues - Resolve

Startup Issues - Resolve (2)

Startup Issues - Resolve (3)

Startup – Black screen with cursor