This may work if the drive is OK. If it's accessible but corrupted try the second procedure.
Reinstall Lion, Mountain Lion, or Mavericks without erasing drive
Boot to the Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
Repair
When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported then click on the Repair Permissions button. When the process is completed, then quit DU and return to the main menu.
Reinstall Mountain Lion or Mavericks
OS X Mavericks- Reinstall OS X
OS X Mountain Lion- Reinstall OS X
OS X Lion- Reinstall Mac OS X
Note: You will need an active Internet connection. I suggest using Ethernet
if possible because it is three times faster than wireless.
Install or Reinstall Mavericks or Mountain Lion from Scratch
Be sure you backup your files to an external drive or second internal drive because the following procedure will remove everything from the hard drive.
OS X Mavericks- Erase and reinstall OS X
OS X Mountain Lion- Erase and reinstall OS X
OS X Lion- Erase and reinstall Mac OS X
Note: You will need an active Internet connection. I suggest using Ethernet if possible
because it is three times faster than wireless.
And, it neither work consider my original suggestion.
