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This usually happens if there is any issue with the system files or hard drive. We can try some basic troubleshooting steps and see if it works or not.
Solution 1 :
First reset the PRAM (it is a temporary memory) of your Mac. Follow the steps below to reset the PRAM and NVRAM
Shut down your Mac by holding down the Power button for 5-10 seconds.
Restart and immediately hold down Command-Option-P-R keys at the same time
Hold the keys down until the computer restarts and you hear the startup sound for two or three times.
Release the keys and let the Mac bootup.
Solution 2 :
If that didn't work, then turn off your Mac. Turn it back on and immediately hold down Shift key on your keyboard for 15 seconds and this will boot into Safe Mode. It will take up to 30 minutes to boot into Safe mode. If it is not booting into Safe Mode, the move to next solutions.
Solution 3 :
Turn off your Mac by holding down the Power button for 10 seconds to turn it off. Turn it back on and immediately hold down Command and R keys at the same time for 15 seconds and this will boot your Mac to the Mac OS X Utilities screen.
From there, click Disk Utility. Select your hard disk at left column (Macintosh HD or hard disk name). Then click Verify Disk (under First Aid). If asked to repair, click Repair Disk. Then click Repair Permission.
If you are using latest Mac OS X El Capitan, then you will not see Repair Disk option in Disk Utility. Instead click First Aid button and run it. Repair if asked. Restart from your Mac from Apple menu.
Solution 4 :
Restart your Mac and immediately hold down Command and R keys at the same time for 15 seconds and this will boot your Mac to the Mac OS X Utilities screen. From there, click Reinstall Mac OS X. Then follow the instructions to reinstall your Mac OS X.
(If that didn't work, then restart your Mac and immediately hold down Command, Option and R keys at the same time for 15 seconds and this will boot your Mac to installation screen. Follow the onscreen instructions to reinstall)
Please let me know if that didn't work, so we can continue troubleshooting. I will send you instructions in here, so you can take your time and do this at your convenience.
Turn off your Mac completely by holding down the Power button for 10 seconds.
Plug in the MagSafe power adapter to a power source, connecting it to the Mac if not already connected.
On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
Release all the keys and the power button at the same time.
Press the power button to turn on the computer and immediately hold down Option key on your keyboard. Does it boot into any screen ?
If so and if you see Recovery HD on the screen, then select it and press return. This will boot into OS X Utilities screen. Reinstall OS X from there.
If it still not working, then I want you to keep trying the 4 the solution to boot into OS X Utilities. It is the only way to reinstall the OS X to fix the problem unless the hard drive of your Mac is failing. If it is the hard drive, then you will have to take it to the Apple Store to get the drive replaced. If it is less than 1 year old, then Apple will replace the hard drive or fix all components for free.
If it is out of warranty, then it will cost around $150-$200 to replace the hard drive. Try the 4th solution and let me know the results please.