A few questions:
- Do you have an external hard drive with backup of the internal hard drive? If not it might be a good idea to try and get one incase you have to erase the internal hard drive...a good source is OWC, I have three of their Mercury Pro Elite 2 TB drives.
- Have you tried starting up in Safe Mode - startup holding the shift key, if you get a good startup then there may be issues with applications of extensions that Disk utility cannot resolve.
- If there is physical damage to the hard drive, the only options will be a new hard drive or an erase and install of the operating system, and all applications, so that the bad sectors can be avoided. This step should not be done until you have a backup of the drive.
Another idea: You might be able to fix this by running fsck in Single User mode. You would repeat this until possibly it is able finally to make the repairs. It's worth a try anyway.
Use fsck if necessary