WARNING: BE SURE YOU HAVE UNPLUGGED ANY COMPUTER BEFORE YOU WILL BE ADDING/REMOVING PARTS TO/FROM!
Can you install that old drive into your new computer? If so, don't worry about formatting it just yet. Simply take out that old drive and place it in the new computer. I recommend you naming it before doing so, so it's easily recognized once installed in the new computer.
Once that old drive has been installed into your new computer and you see it listed after you have logged into Windows, you can simply format the drive then. This may help you. http://windows.microsoft.com/en-US/windows-vista/Formatting-disks-and-drives
Also, there are plenty of programs out there that you can use to format your drive with, if you feel the desire to do so. I'll leave that to you to search for them.
Remember, give your additional drive(s) a name to help you easily identify them in Windows Explorer.
Hope this helps you. Good luck and let us know how things turned out.