If Windows can't read the drive, then Ubuntu most likely won't be able to either (though there may well be tools included in the distribution which might be able to help, I wouldn't recommend going near them if you don't know what you're doing). If anything, Ubuntu's support for NTFS partitions is a lot worse than Windows (since only Windows formats its drives as NTFS).
My advice is to not worry about using Ubuntu. Unless you find some really good drive recovery software which only runs on Linux, there's not much benefit to it unless you're an experienced Linux user who's happy to muck around on the command line, edit system files, etc.
Ubuntu and Windows read drives the same way, afaik. I don't see how it would recognize data just because it's a Linux distro. So, what Bob2004 said, except for the NTFS part, which I don't recall OP ever mentioning. Ubuntu has enough open-source NTFS support to be able to create, resize, and read from/write to NTFS partitions, IIRC.
If you insist, though, any version of it is fine; I'd just go with the latest version 11.10. If you want guaranteed stability, grab 10.04, which is their LTS version released in April 2010. Just make sure you grab it from the Ubuntu site (if you insist on torrenting it, they have torrent files available in their alternative downloads page). Grab the x86 version, always. Pop it in, mash F12 while booting (if you have boot from CD first in your BIOS settings you don't have to do this), boot from CD. Click "Try Ubuntu" when it asks if you want to install. Make sure you only click it once, as I've had system hangs from clicking it more than once. Oh, and to answer your question, Ubuntu is a desktop OS. It's very possible to use it without ever using the command line, like Windows.
11.10 is Unity-based, so things are much different from the classic GNOME desktop, which 10.04 should be using. I've been using it for a few months, so I kinda know my way around. Hit Ctrl+Alt+T (I think) to start a terminal. The file browser GUI program is at the very top of the menu on the left, just below the black icon (which is Dash and acts a lot like the Windows 7 Start search box). If Ctrl+Alt+T doesn't open a terminal, you can type terminal into Dash to start it.
Note: For this walkthrough I will assume you are using 11.10/Unity. If you're using 10.04/GNOME classic, check the bottom of this post.The first thing to note while running off an Ubuntu Live CD is that none of your hard drives are mounted, but they should be detected. Use Dash to open GParted to see what hard drives are connected (don't worry, if you don't tell it to do anything to your drives, it won't actually do anything - I'm sure Meomix hasn't actually used GParted before). Use the drop down list at the top right to select different drives (named sdx, where x is a lowercase letter starting from a). You can see what a drive's contents look like - if its data is readable, it will show a summary of the partitions available and colors representing the amount of space used.
Since your backup drive is new, it will likely have nothing on it, and therefore the entire bar will just be gray and say "unallocated." Since you can't use dd to clone your disk, you'll have to format it so you can use it. Go to Partition -> New to create a new partition table with default settings (MS-DOS). Next, right-click on the bar of unallocated space, and create a new primary partition. Be sure to use FAT32, or NTFS if you have files over 4GB on your 1TB disk. All the default settings should be fine; just make sure you allocate the entire disk. To apply your changes, click the green checkmark (nothing actually happens to your disk until you click that, and confirm that you want to do what you want to do).
Once you have your 1TB drive connected, open up GParted the same way and look for the disk. If the disk shows up as unallocated, you probably can't read it, but it doesn't hurt to try anyway (if you see a red circle with "!" in it, you might have a chance). First thing to know is what filesystem is on your disk, as the mount command probably won't be able to detect it (if Windows couldn't, Ubuntu probably can't either). Also note the sdx ID of the drive in GParted.
See the extra post below before continuing.Open up a terminal, and type the following command:
sudo mount -t <filesystem> /dev/sdx /media
Be sure to replace <filesystem> with your filesystem, like FAT or NTFS, and replace sdx with your drive, which will probably be sda or sdb.
Here's an example command, note that your filesystem input should be all lowercase:
sudo mount -t fat /dev/sdb /media
The above command will mount the sdb drive in the /media directory with filesystem FAT. FAT12/16/32 is auto-detected; if you want to override auto-detection to 32, I believe the command is:
sudo mount -t fat fat=32 /dev/sdb /media
If it just quietly mounts, you're in luck. If it throws an error regarding the filesystem being invalid, you're not so lucky. If it complains about the filesystem being read-only or something, you might be in luck.
Edit: For the below command, as noted in the post below, change "/media" to your desired directory.
In the terminal, type:
(that second line is LL in lowercase)
This will move you to the mount point and list everything in the directory in long listing format. If it only shows ./ (which means current directory) and ../ (which means parent, or 1-up, directory), either the mount failed, or you can't read anything on the drive.
(If command ll doesn't work, use "ls -l" - those are all lowercase L)
If you can read anything on the drive at all, open up GParted again and find your backup drive. Note the sdx. Mount that disk with the following command (assuming it's already formatted):
sudo mount -t <filesystem> /dev/sdx /mnt
This will mount your backup disk to /mnt.
Finally, run the command:
This will copy everything in the /media folder, where your 1TB disk is mounted, into your /mnt folder, where your backup disk is mounted. Make sure you don't touch anything in the terminal until the command prompt comes back up, which is that little bit of text that ends with ">". It'll probably be pretty boring to watch the cursor flash for a few hours, so you'll probably want to do something on another computer or start a browser or something, or even take a nap.
Edit: As with the mount commands, change these directories to the ones you actually want.
When you're done everything, run the following two commands to unmount your disks:
sudo umount /media
sudo umount /mnt
And then close everything and shut down by finding it on the menu that opens when you click at the far upper-right of the screen. Or, if you want, the command to shut down is:
The 0 specifies the time delay, in seconds, between your issue of the command to the actual shutdown.
Finally, if you are running GNOME classic desktop for any reason, the aforementioned programs are located at:
Terminal: Applications -> Accessories -> Terminal
GParted: System -> Administration -> GParted
File browser: Places -> Computer
There is no Dash in GNOME classic.
These can be found in the menus at the upper left of the screen.