Cannot partition, erase, format or restore (OS X Lion, MBP 2009)

Question

Hi!
I have a 2009 MacBook Pro 13" (2.53 / 4GB / 250GB / Lion) that stalled on the grey screen + spinning wheel a few months ago. I was able to recover my data and load it onto a new MBP, so I set the old one aside. I am now trying to repair the problem and cannot get past DiscUtility.
Starting with a Cmd+R start:
"Use English for the main language" [press Enter]
Mac OS X Utilites
[Double-click Disc Utility]
I no longer have "Macintosh HD," but instead a volume called "disc0s2."
From the First Aid tab, I can click Repair Disc. It states: Verifying and repairing partition map for "ST9250315ASG Media" and the time bar begins to run across, while the details box does 5 checks (prereq's, partition list, EFI system), and begins "Repairing the EFI system partition's file system" This runs for a seemingly endless amount of time, until the mouse changes from arrow to spinning color wheel. At this point, clicking nothing works, but the mouse still moves. I manually restarted after 25 minutes. I can let this go all night, but I would like to continue trying alternatives.
For Volume, the error reads:   
     Volume Erase Failed
     Volume Erase failed with the error:
     File system formatter failed.
For partition, I have:
     Partition Layout: Current
     Partition Information:
          Name: disc0s2
          Format: Mac OS Extended (Journaled)
          Size: 249.2 GB
From here, when I try to set up one partition, renamed "Macintosh HD" still journaled for the total capacity (250.06GB), I get:
     Partition Failed    
     Partition failed with the error:
     Couldn't unmount disc.
And then....
Starting with a Cmd+R start:
"Use English for the main language" [press Enter]
Opened Terminal to verify "date" is correct, which it is. Close Terminal.
[Double-click on Install Mac OS X Lion]
[Click Agree]
The only option I have to install it on is "Recovery HD." It has 650MB total, with 140.3MB available. Also states, "This disc is locked."
I cannot click on the disc anyways, and the only available option is 'Back.' Ultimately, I have to exit Install, and I'm back to the Mac OS X Utilities.
So, could it be a bad drive? It would seem impossible to me considering that any of this is working at all. I have also tried to boot from a OS X Mavericks USB drive (from my newer MBP), but with the same results; except that the Install OS X is for Mavericks. Everything else is exactly the same.
I don't need any of the data on the computer (if there is any left anyways), and I'll try just about anything.
Thank you in advance for your time!

Answer 1

Thanks for the quick reply. I'm afraid that might be true. Can the computer operate like this with a bad HD?
Also:
For partition tab, I have:
     Partition Layout: Current
     Partition Information:
          Name: disc0s2
          Format: Mac OS Extended (Journaled)
          Size: 249.2 GB
From here, when I try to set up one partition, renamed "Macintosh HD" still journaled for the total capacity (250.06GB), I get:
     Partition Failed   
     Partition failed with the error:
     Couldn't unmount disc.