First reset the SMC:
Shut down the computer.
Plug in the MagSafe power adapter to a power source, connecting it to the Mac if its 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.
Note: The LED on the MagSafe power adapter may change states or temporarily turn off when you reset the SMC. This much came from Apple's SMC reset insructions for you model: http://support.apple.com/en-us/HT201295.
Next, try the four-finger salute. The technical name for that maneuver is "resetting the NVRAM". To try it, be sure the computer is completely shut down, then disconnect everything from the computer except power cable.
Press the power button to start the computer and immediately hold down all of the following 4 keys as quickly as you can: command, option, P, and R (the maneuver used to be called "resetting parameter ram", hence the p and r). You may need both hands on the keyboard until you¹ve done it closer to as many times as I have.
Keep those keys down until you hear the startup chime at least 3 times. It could take a minute or so, depending on the machine. The screen usually lights and goes dark again between chimes.
When you’ve heard enough chimes, wait for one more. As soon as you hear it, release the keys and instantly press and hold shift. As soon as the Apple appears, let go of the shift key. That puts it in safe boot mode which also runs a file system check. If booting is still a problem, another clean install for OS X may be needed, and faulty hardware is still suspect.