Keep in mind that if the drive is "dying", there might be issues when trying to use a complete drive-cloning utility. I think that what you're looking for isn't actually a "clone", what you need is data recovery.
You want a fresh installation of XP on the new drive, not a copy of the already-corrupted installation from the bad drive. Then you want to copy whatever data files you can save off of your old drive onto the new drive. (Just data, no programs or OS files.)
I had a very similar situation where a friend had a dying laptop drive, and they wanted to rescue the important data files and photos off of the drive. The dying laptop would not boot at all.
Based on a piece of advice from a data recovery thread on this very BBS, I used the product
Trinity Rescue Kit. I made a bootable CD of the Trinity Rescue Kit, popped it in the dead laptop, plugged in the "good" external USB drive, booted into the Trinity CD, and typed the following:
mountallfs
mc
...and got a great text-based UI for copying files to the good USB drive quickly and painlessly. It's now one of the favorite tools in my arsenal.