The software doesn't use license keys. If you normal launch from the website, make sure to login before launching the app to access the paid features.
You use your login for the website to upgrade the installed application.
If you use use the full app installation, first install the full app by downloading from this page:
If you have a Solo Plan, after installing click the "Recorder" button and enter your email address and password to upgrade.
If you have a Team Plan, after installing launch the app and click the Team Plan button then enter your Team Plan access url.