Start-Up: Folder with gray question mark / Disk Utility: Invalid Sibling Link

Yesterday, I was working on my computer and it froze up. My only option was to reboot by holding down the power key. When the computer restarted, the screen was all grey with a folder in the middle of the screen with a question mark.
I tried the following:
1) Boot up computer while holding down the "Option" key. - Didn't work.
2) Boot up the computer while holding down the "Shift" key. - Didn't work.
Since the first two options didn't work I inserted the original system install disk and booted up while holding down the "C" key. I selected "English" as the language and then opened "Disk Utilities." I pressed "Repair disk" within First Aid. The message I am getting is as follows:
"First Aid failed. Disk Utility stopped repairing "Macintosh HD" because the following error was encountered: Filesystem verify or repair failed."
The details screen shows the following:
"Verify and repair volume "Macintosh HD"
Checking Journaled HFS Plus volume.
Checking Extents Overflow file.
Checking Catalog file.
Invalid sibling link.
Rebuilding Catalog B-tree.
The volume could not be repaired.
Error: Filesystem verify or repair failed."
I ran the "Repair disk" function about 6 times but it was not successful.
I was then going to try to do an "Archive and Install" from the original system disk but when I go to do that no destination options appear at the "Select Destination: Where do you want to install Mac OS X?"
I have not backed up my data very recently (and a lot of what I have stored on this computer is work - I am a freelance designer) so I would like to do something that at least allows me to transfer my data off of my hard drive before reformatting or anything like that. Of course, if there is a less intrusive fix that can leave my hard drive in tact, that would be ideal.
Any advice? Tips? Solutions? I have a MacBook Pro, 15" that I purchased 3 years ago (my 3 year Apple Care plan just expired about a month ago).

You are in a tough situation.  The disk appears unusable according to Disk Utility.  As was suggested you may (only may) be able to salvage it with Disk Warrior (not sure about Data Rescue).  DW can sometimes recover a drive that DU can't.  But nothing else can be suggested. 
If you can get that disk recovered then back it up ASAP, wipe the disk, reinitialize it, and verify it.  But I'm the paranoid type, and with the kind of errors you show for that disk, I am not sure I would ever trust it again.  At most I would relegate it to a scratch disk.
Note, if it is a drive that you bought, most drives have a 3 to 5 year warrantee period, so you could get it replaced by the manufacturer if it is within that warrantee period.