As was always the case, you need a key file to run the licensed version of Terragen. Nothing has changed in that regard. Your key file has not been sent to you yet, just give is a few minutes and we'll send it to you. In the future the process will be more automated but for now the key file generation still needs manual intervention.
Regarding your error message, first we can't see the image you linked to because it's referencing a file on your local hard drive (you can see it but nobody else can); please use the Attachment function when posting. Second, it sounds like you may have some Terragen environment variables setup which point to your old TG2 install. If so, you should update them to point to TG3.
- Oshyan