Are you sure that you ever had the product key?
New computers are often sold with Microsoft Office installed but without the necessary licence. If you actually want to use Microsoft Office you have to purchase a licence (which provides you with the product key). The licence costs (at discounted prices) around a hundred quid!
It might be simpler to forget about Microsoft Office and use a free alternative. The most popular is OpenOffice (which is used by many schools, councils, police forces and other public bodies who don't like paying massive licence fees to Microsoft):
http://www.openoffice.org/
(If you use OpenOffice, but want others to be able to open your word-processed documents in Microsoft Office, you should change the OpenOffice default 'Save' option so that everything will automatically be saved in the correct format. See here:
http://voices.yahoo.com/how-set-openoffice-writer-save-as-microsoft-11017880.html ).
Other free alternatives are LibreOffice (which is based upon the source code for Lotus, and is widely praised in the computing press):
https://www.libreoffice.org/
and Kingsoft Office (which has only recently been brought to my attention but which has very good reviews):
http://www.kingsoftstore.co.uk/kingsoft-office-freeware.html
Chris