|If the hard drive is physically broken then there is not alot that can be done. Sometimes if it is clicking or not powering up you can throw it in the freezer for a few hours and then try starting it up.|
If the issue is software related then there are a few options that you have to get the hard drive going. Boot with a windows Install cd and exit to the repair option and choos chkdsk /r then chkdsk /p then fixboot.
If your set on cloning the hard drive i would suggest downloading a copy of Hiren's boot CD (similiar to Bart's PE) He has included a free cloning program with his software. Essentially you start the computer with the cd and both hard drives attached. You run/extract the clone program from the start menu and you choose the source drive and then the destination drive. Be sure to choose the right drives.
If you just want to backup the data from that hard drive then booting from that CD will allow you to copy the contents from it to another drive (USB or physical hard drive)