It seems most likely that the hard drive and the file system is damaged and it is not possible to mount the drive in the normal way. The Ubuntu LiveCD will have no problems reading a good NTFS partition - it will be accessible through Nautilus File manager.
If the Windows file system does not show up in Nautilus, try mounting the drive as read only. Open a terminal window and type:
sudo mount -r -t ntfs /dev/sda1 /mnt
(replace /sda1 by the name of your Windows partition, you can check it via 'sudo blkid' or 'sudo parted -l')
If this works with no errors you can then access your data in terminal or Nautilus under the directory /mnt, for example
cd "/mnt/Documents and Settings/yourusername/Documents"
and so on. If you use terminal (bash) then be aware that Linux is case sensitive. If you type 'documents' instead of 'Documents' it will not work.
You will not be able to modify anything on the hard drive because it will be mounted read only. This is a good thing given the current state of the drive. You will need another hard drive with enough capacity make your backup on.
If the mount works but the contents of /mnt don't look right, it might be because it's the wrong partition (the above assumes windows installed on the the first (sda1) partition. If you can't find the correct partition then paste the output of the following bash command here:
sudo fdisk -l
so that we can have a look.