First, you don't have a Recovery partition on the boot drive, which you should have. If your model is capable of it, boot into Internet Recovery and reinstall OS X.
Computers that can be upgraded to use OS X Internet Recovery
If you still have the problem after reinstalling, proceed as below.
If you have more than one user account, these instructions must be carried out as an administrator.
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.
Step 1
Make sure the title of the Console window is All Messages. If it isn't, select All Messages from the SYSTEM LOG QUERIES menu on the left. If you don't see that menu, select
View ▹ Show Log List
from the menu bar.
Enter "BOOT_TIME" (without the quotes) in the search box. Note the timestamps of those log messages, which refer to the times when the system was booted. Now clear the search box and scroll back in the log to the last boot time when you had the problem. Select the messages logged before the boot, while the system was unresponsive or was failing to shut down. Copy them to the Clipboard (command-C). Paste into a reply to this message (command-V). Please include the BOOT_TIME message at the end of the log extract.
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. In most cases, a few dozen lines are more than enough.
Please do not indiscriminately dump thousands of lines from the log into this discussion.
Important: Some private information, such as your name, may appear in the log. Anonymize before posting.
Step 2
Still in Console, look under System Diagnostic Reports for crash or panic logs, and post the entire contents of the most recent one, if any. In the interest of privacy, I suggest you edit out the “Anonymous UUID,” a long string of letters, numbers, and dashes in the header of the report, if present (it may not be.) Please don’t post shutdownStall, spin, or hang logs — they're very long and not helpful.
