Either your drive is failing or has been corrupted. Please try the following. You cannot do the following unless you have purchased Lion or later. From your post that's not clear. Without knowing your exact model I cannot tell you what to do.
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 Lion, 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.
If your computer is a 2010 or earlier model, then you should be able to do the following:
Reinstall OS X without erasing the drive
1. Repair the Hard Drive and Permissions
Boot from your Snow Leopard Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu. 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 click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer.
If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.
2. Reinstall Snow Leopard
If the drive is OK then quit DU and return to the installer. Proceed with reinstalling OS X. Note that the Snow Leopard installer will not erase your drive or disturb your files. After installing a fresh copy of OS X the installer will move your Home folder, third-party applications, support items, and network preferences into the newly installed system.
Download and install Mac OS X 10.6.8 Update Combo v1.1.
