Apple software not updating - Error message

Question

iMac locked up (white screen of death) so restarted.
When it restarted it will no longer update apple applications through the App Store.  Downloads and then starts to instal and comes up with an error message.   (iTunes, iMovie so far) 
Non Apple programs still seem to update and/or instal.
Applications still run but not update to new versions.

Answer 1

Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Console in the icon grid.
Select
          /var/log ▹ install.log 
from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar at the top of the screen. The contents of the log will appear on the right. Each log message begins with a timestamp. Select the messages from the time of the last installation or update attempt. If you're not sure when that was, click the Clear Display button in the toolbar of the Console window and then try the installation again. Select the new messages that appear. Copy the messages to the Clipboard by pressing the key combination command-C. Paste into a reply to this message (command-V).
☞ If there are runs of repeated messages, post only one example of each. Don’t post many repetitions of the same message.
☞ When posting a log extract, be selective. Don't post more than is requested.
☞ Please don't indiscriminately dump thousands of lines from the log into this discussion.
☞ Please don't post screenshots of log messages—post the text.
☞ Some private information, such as your name, may appear in the log. Anonymize before posting. You may need to use a text editor with search and replace, such as TextEdit.