click the start button, right click on computer and go to properties. At the bottom of the window click on change key. Type in the new key that you bought and then register it.
I do this all the time at work, Install a computer with a disc I already have. After a few weeks if everything is working fine ill order a new copy of the OS and put that key in for the computer. Haven't had an issue yet to this date, as long as you buy the same version as to what you install you will be fine.