not sure why you think you'd need to boot a live os, unless i'm misunderstanding and it's your os drive that has problems and not the external hd.
i think if i were you i'd install ntfsfix on your linux system and use that to try and repair the problem, failing that then i'd use a windows pc to run chkdsk from or a windows os install/repair disk.
curious but what software recommends running chkdsk -f to fix the ntfs file system problem on a linux pc, never seen such a thing myself seeing how chkdsk is a windows command and nothing to do with linux as far as i'm aware?
best advice is probably this.
If the computer has nothing but Linux, you should not be using NTFS. There are no good Linux tools for repairing NTFS damage. (The Linux ntfsfix tool just does some very basic checks and then flags the filesystem as needing more attention from Windows.) Thus, in the long term your goal should be to switch from NTFS to a Linux-native filesystem. In the short term, you should use a Windows emergency disk to repair the filesystem. (Such emergency disks are widely available, but I don't happen to have any URLs handy. Maybe you can find one by searching Microsoft's site.) It's conceivable that you could use ntfsclone to make a backup, too; see the –rescue option in its man page. I've never tried this, though.
Overall, I'd say you should do the following:
Use a Windows emergency disc, ntfsclone, or any other tool necessary to gain access to the partition.
Copy the files from that partition to another disk. You can do this in either Linux or Windows, depending on what's convenient and how you got access to the disk.
Create a Linux-native filesystem (ext2/3/4fs, ReiserFS, XFS, JFS, or maybe even Btrfs) on the partition.
Copy the files back to the original (but freshly-prepared) partition.
Good advice Terry. NTFS is not an open platform, so everything Linux does with NTFS is just a reverse engineered hack so to speak. Not that it won't work, but it is not safe to run Linux based tools on NTFS.
To answer your question about repairing an NTFS file system. The likely easiest thing for you to do is plug it into a friend or neighbor's computer and repair the file system in Windows. Surely you know somebody close by with Windows?