There are six versions of Vista - Ultimate, Enterprise, Business, Home Premium, Home Basic and Starter. Provided that the disc you have is the same version as the one presently installed you should have no problem in using it with the license key on the tower case. You may have to re-activate it with Microsoft after installation and sometimes they may give you a phone number to call if activation is a problem, but I have never had any problem if I have to do so. Just have a pen and paper ready when they give out the registration numbers over the phone.
Amazon Fire HD 8 review: A brilliant combination of function and value – with one massive caveat