Then all you can do is to try and make a clone of the drive onto a connected USB drive, if that is possible:
Clone Mavericks, Lion/Mountain Lion using Restore Option of Disk Utility
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.
1. Select Disk Utility from the main menu then press the Continue
button.
2. Select the destination volume from the left side list.
3. Click on the Restore tab in the DU main window.
4. Select the destination volume from the left side list and drag it
to the Destination entry field.
5. Select the source volume from the left side list and drag it to
the Source entry field.
6. Double-check you got it right, then click on the Restore button.
Destination means the external backup drive. Source means the internal startup drive.
Or you can take your chances and reinstall Yosemite:
Reinstall Lion, Mountain Lion, Mavericks or Yosemite 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, Mavericks,or Yosemite
OS X Yosemite- Reinstall OS X
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 isthree times faster than wireless.