Office 2010

Hi All, my computer failed recently & after a diagnostic check showing everything was ok I had to reinstall windows 7 from the Microsoft cd. However, I also have a licensed copy of Office 2010 which I managed to recover from an old backup I made a few years ago. When I ran the setup program it asked for the Product Key which I no longer have or can,t find anywhere. I called Mesh Computers who supplied the computer in 2010 but they have no record of the product key.
I have also accessed the registry hoping the product key would be there but no luck. Any ideas how I can activate office 2010 without the product key. Thanks