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OK restart and hold the Shift key until you see the Apple logo. This will activate Safe boot and it will check the drive for errors among other things. It may take longer to boot and you may see a progress bar during part of the process. If it starts up OK… login then restart the normal way from the Apple Menu. Let me know after.
Reboot into the Recovery HD by choosing the ‘Apple‘ menu > Restart, then hold down the ‘Command’ + R’ keys on the keyboard during the start up process. If you can't get to that menu just hold the power button for 10 seconds until it shuts down. Then start it up again holding those keys. When you see the Apple Logo you can let go.
When the machine boots you may have to choose your language then you will see the OS X Utilities screen. Select the Disk Utility and then Continue. Then in Disk Utility select Macintosh HD in the left column (if there are two with that name or it is named something else choose the first indented item) and then on the right select the First Aid tab then select Run.
It is late here I have to sign off for tonight. If that is ok and you still can't boot do that again but this time choose Reinstall Mac OS X. Let me know.