Unable to install 10.9.5, iTunes 11.4, other system updates on my 2013 Mac Pro

Question

Hi everyone - I'm hoping someone can help me out. My 2013 Mac Pro is currently running 10.9.3. For a few weeks now, I've been trying to get 10.9.4 to install but every time I do, the computer reboots but doesn't actually update. The same is true with 10.9.5 and iTunes 11.4. No matter what I do, including manually downloading the installers (10.9.4 Combo, 10.9.5, and iTunes 11.4), they fail. I suspect that it is a really corrupted permissions issue and I've run the Fix Permissions action in Disk Utility several times but it never changes things.
What's even more confusing is the Updates tab of the App Store app. It shows that I have updates ready and they keep repeating as installed.
Any help is greatly appreciated. As it stands, I'm going to do a totally clean install of Mavericks when it ships but right now, I can't even connect my iPhone 6 Plus to iTunes because it isn't 11.4.
Cheers,
Brian

Answer 1

I would suggest:
Repair the Hard Drive and Permissions - Mavericks, Lion/Mountain Lion
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. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
Repair
When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list.  In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive.  If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported then click on the Repair Permissions button. When the process is completed, then quit DU and return to the main menu. Select Restart from the Apple menu.
If this does not work, then try reinstalling OS X instead which will automatically install the current version:
Reinstall Lion, Mountain Lion, or Mavericks without erasing 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. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
Repair
When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list.  In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive.  If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported then click on the Repair Permissions button. When the process is completed, then quit DU and return to the main menu.
Reinstall Lion, Mountain Lion, or Mavericks
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.