Macintosh HD disappeared from finder after "disk damaged and cannot be repaired"

I have a MacPro 13.3 Inch mid2011 with 500GB storage and recently while performing a Mac update, it froze and was still stuck on a grey screen even after multiple restart attempts. I finally tried Command+R to attempt Time Machine(none were available), Disk Utility but "Repair Disk" was greyed out, and finally tried to reinstall Mac OS X but when it was close to completion, again, it showed Macintosh HD is damaged.

I bought an external hard drive hoping to save my school work from Macintosh HD

• Disk Utility>External Hard Drive>Partition>GUID Partition>Mac OS Extended
  
  
  
  2. Ran OS X Installer and selected my External Hard Drive as the target. Near completion, it gave me the option of transferring my information from another drive. I selected the first option (Mac etc), but when it came to loading my internal drive, it didn't load. I let it run for several hours but still to no avail so I skipped the process and finished registering.
  
  
  3. When my Mac loaded, it showed the message that Macintosh HD is damaged. Please back up your files immediately.
  
  
  4. I loaded Finder, but Macintosh HD is not listed under devices.
  
  
  5. I loaded Disk Utility and at first it showed my Macintosh HD with my 69GB/500GB...but then it disappeared after I clicked on Verify Disk.
  
  
  6. If I unplug my External Hard Drive, Mac shows a grey screen with a folder and question mark. 6.
  
  
  
  

Is there anyway of recovering the data on my Macintosh HD now?

If I don't replace the hard drive and just continue to operate using my external hard drive will that work? I am not sure whether it's better to just get a Thinkpad or repair/replace the internal hard drive.

I appreciate all help and advice you can offer! Thank you