Unless you have install discs for the windows 2013 and the product key, I doubt you will have success with what you want to do. I suspect the old laptop came with it offered, you paid after the trial period and got a key then for it. You could try Jellybean Product Key Finder, maybe that will access it.
I just bought a new laptop and I need to know how to transfer over my already purchased Microsoft Office 2013 to my new laptop. I don't have the code nor recall how I even purchased it because I had my old laptop for a very long time. Is there a way to do this?