Download the ISO for this Linux version.
This link will start the download:
http://releases.ubuntu.com/10.04.3/ubuntu-10.04.3-desktop-i386.iso
Once the download finished take the ISO and burn the contents to a CD. That will make the bootable Linux Live CD.
EDIT: you can use this software to burn the ISO if you do not have a program to do so already
http://www.imgburn.com/index.php?act=download
Take the live CD and put it in the DC//DVD drive. Power on the pc. There will be a menu. There will be an option that will say something like Try Ubuntu. This will boot Ubuntu without making any changes to the Hard Drive.
Once the Operating System is booted you can access the Hard Drive from there. I can give you a bit more help when you get there.
EDIT: a bit more information on accessing the drive.
In Ubuntu there is a top menu that has Applications Places and System. Places will have all of your files and folders in it. A bit down the list there should be a drive that is labeled with a bunch of letters and numbers. Mine is something like 0082E6AF82EE6A7. That is your hard drive
Since the drive is not being recognized by windows you may need to boot the Live CD a few times to get it mounted correctly. I think I tried 3 or 4 times before I got it when I did recovery for a friend.
If the drive mounts correctly and you can access the data on the drive you
should be able to get to your files and transfer them off. (this all depends on the drive cooperating with you)
In order to get to your files you need to go through your folders and find the folders that hold your files. I have a windows 7 system that I access so for me I can get to the folders by going through (hard drive)/Users/My User name (yours will be different). The "/" between the different files indicate different folders that I went into to get to the next folder.
*
NOTE* The path that I used to get into my files were for my Windows 7 system. Windows Vista and XP may have a different path that you will need to use but the concept will still be the same.
Once you access your folder that is labeled with your user name you should see your documents, music, pictures, desktop, downloads folders along with a lot of others that are of no importance to you for data recovery. When you go into the folders (like Documents) all of your files will be there for you to take to another location. Just copy and paste to the new drive.
The transfer may take a while being that the drive is barely working if at all.
If the drive no longer reads or un mounts itself it may be a good idea to give it a break and let it cool for a while. While I was doing this every day or so I had to turn it off for a night and get it remounted in the morning.
I hope this works! It would be great to see all of the data get rescued. Good Luck and as always, if your have any questions I will be more than happy to explain any of the steps in better detail.