Failed boot

See OS X- Gray progress bar appears under Apple logo during startup. You may have success doing the following:

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.

On the drive that will not boot and reports directory errors:

You have 350,000 files that belong to Mac OS X, and your photographs. It is much easier to find your photographs than to have every Mac OS X file be right enough for booting.

Yes, get a new drive that is a candidate for replacing your current drive (and an enclosure), and yes, Install Mac OS X on it from fundamental sources, and yes, boot your Mac from that external drive. Now you can get something done, and you can use the full power of Mac OS X (and additional Utilities if you need them) to attempt to retrieve your Photos.

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Backup is SO MUCH Easier than FIX-UP.

Your current drive has an error that Disk Utility cannot fix. But it may be fixable by Disk Warrior if you are willing to give it a try. You can download a trial that will let you know if the drive is recoverable, but you would then have to purchase the license in order to actually repair the drive. If DW says it cannot fix the drive, then you are not out any money as yet. You may be able to recover your files using other software:

General File Recovery

If you stop using the drive it's possible to recover deleted files that have not been overwritten by using recovery software such as MAC Data Recovery, Data Rescue II, File Salvage or TechTool Pro. Each of the preceding come on bootable CDs to enable usage without risk of writing more data to the hard drive. Two free alternatives are Disk Drill and TestDisk. Look for them and demos at MacUpdate or CNET Downloads. Recovery software usually provide trial versions that enable you to determine if the software would help before actually paying for it. Beyond this or if the drive has completely failed, then you would need to send the drive to a recovery service which is very expensive.

The longer the hard drive remains in use and data are written to it, the greater the risk your deleted files will be overwritten.

Also visit The XLab FAQs and read the FAQ on Data Recovery.

You can replace the drive in the computer and put the old drive into an external USB enclosure to try recovering your files if possible.

Best I can offer at this point.

Yes, any 3.5" SATA drive will work internally.

Get an SSD.

16MB cache drives are old and have not been used in years, most today have 64MB cache and are SATA III which is fine. Same goes for SSD just need a sled adapter but the best $130 + adapter you could do.