After more HD disasters than this old tech is willing to remember or recount, let me give you my take on the subject. Eh?
To preserve everything on your old HD, either take it completely out of your PC or at least unplug it so the motherboard can't see it.
Connect your new drive and make sure your BIOS sees it correctly and then do a clean install of your OS to the new drive.
The old drive DOES NOT enter into this process anywhere!!!
Once the OS is properly installed and running correctly, then connect the old drive as a slave drive in the system. With IDE drives, make the old one a SLAVE drive. With SATA drives, connect the old drive on the #2 SATA port, with the new drive on the #1 port.
Sata drives will always boot from the lowest numbered port first, assuming it has an OS and a boot sector.
With the new drive booting the PC and the old drive set up as a slave drive, you can use Windows Explorer to transfer any data files you want from the old drive to the new one. Programs will have to be reinstalled, along with printers and any other peripherals.
This somewhat long winded process will assure that you DO NOT wind up reformatting your old drive and erasing all your data, and that your OS does not install to the wrong drive.
I speak from some very bad experiences, so learn from my mistakes. Eh?
PS: If I were doing the job in my own shop, I'd take an entirely different tack. First I'd determine whether the old HD was truly failing or not and if it contained any data errors or NOT. Running Chkdsk /f/r can ferret out any data errors and usually fix them.
A hard drive repair program like "Spinrite 6" can usually find any bad spots on the HD and move any data in those spots to a safe location.
Finally, after determining that the data files are OK, I'd just clone the old drive to a new one. Then keep the old drive as a backup.
Doing it that way, nothing would be lost and no programs or drivers would have to be reinstalled.