Take each of these steps that you haven't already tried. Stop when the problem is resolved.
The first step in dealing with a boot failure is to secure your data. If you want to preserve the contents of the startup drive, and you don't already have at least one current backup, you must try to back up now, before you do anything else. It may or may not be possible. If you don't care about the data that has changed since your last backup, you can skip this step.
There are several ways to back up a Mac that is unable to boot. You need an external hard drive to hold the backup data.
a. Boot into Recovery by holding down the key combination command-R at the startup chime, or from a local Time Machine backup volume (option key at startup.) Release the keys when you see a gray screen with a spinning dial. When the OS X Utilities screen appears, launch Disk Utility and follow the instructions in the support article linked below, under “Instructions for backing up to an external hard disk via Disk Utility.”
b. If you have access to a working Mac, and both it and the non-working Mac have FireWire or Thunderbolt ports, boot the non-working Mac in target disk mode by holding down the key combination command-T at the startup chime. Connect the two Macs with a FireWire or Thunderbolt cable. The internal drive of the machine running in target mode will mount as an external drive on the other machine. Copy the data to another drive. This technique won't work with USB, Ethernet, Wi-Fi, or Bluetooth.
c. If the internal drive of the non-working Mac is user-replaceable, remove it and mount it in an external enclosure or drive dock. Use another Mac to copy the data.
Press and hold the power button until the power shuts off. Disconnect all wired peripherals except those needed to boot, and remove all aftermarket expansion cards. Use a different keyboard and/or mouse, if those devices are wired. If you can boot now, one of the devices you disconnected, or a combination of them, is causing the problem. Finding out which one is a process of elimination.
Before reconnecting an external storage device, make sure that your internal boot volume is selected in the Startup Disk pane of System Preferences.
Boot in safe mode.* The instructions provided by Apple are as follows:
Shut down your computer, wait 30 seconds, and then hold down the shift key while pressing the power button.
When you see the gray Apple logo, release the shift key.
If you are prompted to log in, type your password, and then hold down the shift key again as you click Log in.
Safe mode is much slower to boot and run than normal, and some things won’t work at all, including wireless networking on certain Macs.
The login screen appears even if you usually log in automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
*Note: If FileVault is enabled, or if a firmware password is set, or if the boot volume is a software RAID, you can’t boot in safe mode. Post for further instructions.
When you boot in safe mode, it's normal to see a dark gray progress bar on a light gray background. If the progress bar gets stuck for more than a few minutes, or if the system shuts down automatically while the progress bar is displayed, your boot volume is damaged and the drive is probably malfunctioning. In that case, go to step 5.
If you can boot and log in now, reboot as usual (i.e., not in safe mode.) If the boot process hangs again, the problem is likely caused by a third-party system modification that you installed. Post for further instructions.
Launch Disk Utility in Recovery mode (see above for instructions.) Select your startup volume, then run Repair Disk. If any problems are found, repeat until clear. If Disk Utility reports that the volume can't be repaired, the drive has malfunctioned and should be replaced. You might choose to tolerate one such malfunction in the life of the drive. In that case, erase the volume and restore from a backup. If the same thing ever happens again, replace the drive immediately.
This is one of the rare situations in which you should also run Repair Permissions, ignoring the false warnings it produces. Look for the line "Permissions repaired successfully" at the end of the output. Then reboot as usual.
Boot into Recovery again. When the OS X Utilities screen appears, follow the prompts to reinstall the OS. If your Mac was upgraded from an older version of OS X, you’ll need the Apple ID and password you used to upgrade.
Note: You need an always-on Ethernet or Wi-Fi connection to the Internet to use Recovery. It won’t work with USB or PPPoE modems, or with networks that require any kind of authentication other than a WPA or WPA2 Personal password.
Repeat step 6, but this time erase the boot volume in Disk Utility before installing. The system should automatically reboot into the Setup Assistant. Follow the prompts to transfer your data from a backup.
If you get this far, you're probably dealing with a hardware fault. Make a "Genius" appointment at an Apple Store to have the machine tested.
Back up all data on the internal drive(s) before you hand over your computer to anyone. If privacy is a concern, erase the data partition(s) with the option to write zeros* (do this only if you have at least two complete, independent backups, and you know how to restore to an empty drive from any of them.) Don’t erase the recovery partition, if present.