The link I provided before has a 'Getting started' section with a link to another page where you can input your product key. That allows you to create a Microsoft Account. Did you try that? If so, what was the outcome?
If you get no joy from that and you still can't find the details of what your Microsoft Account is (so you can log into that via a link in the 'Download, install, or reinstall' section, it looks like you might have to sign-up for and download a trial copy, from
http://products.office.com/en-us/try. You can then uninstall the old copy (make a restore point first) and reinstall the new one. Assuming it accepts your product key, everything should be OK. You can then opt out of the trial.
Depending on how the new install reacts to your new setup, you may have to reactivate via the 'Activate Office 2013 on a different PC' process outlined at:
https://support.office.com/en-us/art...rs=en-US&ad=US.
If it all goes pear-shaped, at least you can revert to your restore point.