Black Screen in Mavericks with latest update (11.2.2 iTunes)

Question

I've had problems that were never fully resolved regarding waking my iMac from a sleep state. I would be able to hit the volume up and down buttons on my keyboard, hear the tones when the volume was changed, but the screen would remain black no matter what I would do (including resetting PRAM and hard resets, etc.). Eventually I just had to set it so that the computer never went to sleep, and that solved the problem. Or, more appropriately, avoided it.
Anyway... it had been working fine with that adjustment, until this latest software update. Ironically, the update is only for iTunes, so I'm not sure exactly what could've happened. No settings were changed or anything, but here's what it's doing:
The white screen comes up with the apple logo, then the progress bar that shows it's installing the update comes up. It stays up until the progress bar completes, then the screen promptly goes black.
I've tried doing the hard reset thing, or whatever it's called, where you unplug and hold down the power button. And I've also reset the PRAM. Regardless of what I do, every time the iMac reboots, the white apple installation of software screen pops up and tries to reinstall the update again and again. Then it goes to the black screen.
I also tried starting it in safe mode, and even that didn't seem to work, since it's mid-update.
I THINK it may be related to the problem that I was having before (which was not ever solved by bringing my iMac into TWO different apple stores/genius bars), even though I can't test the volume thing... since I think it's getting stuck in the middle of installing the update, and doesn't have the ability to change volume in the middle of all that.
Hopefully this is clear.  Thanks in advance for any help!
PS - There's a slight chance I'm wrong about what the update is. It doesn't make ANY sense to me for it to be doing this obviously OS X update when 11.2.2 is supposed to just be an iTunes update. Perhaps it's the latest of the Mavericks updates and I'm just behind due to being out of town. No way for me to check, since I can't get past the update screen to check that stuff. Sorry!

Answer 1

You can test the startup disk ...
Launch Disk Utility located in HD > Applications > Utillities
Select the startup disk on the left then select the First Aid tab.
Click:  Verify Disk  (not Verify Disk Permissions)
If DU reports errors, restart your Mac while holding down the Command + R keys. From there you should be able to access the built in utilities in OS X Recovery to repair the startup disk.
Make sure to back up all important data first before using OS X Recovery.
If you cannot access the Disk Utility app in /Applications > Utilities
Shut down your Mac then wait about ten seconds.
Then restart while holding down the Command + R keys. Then you can use Disk Utiility from there to repair the startup disk.