Did you actually install the app after downloading? You should go through a dialog with acceptance of the license agreement etc.
Did it ever start at all – the normal sequence is to download, install, start it, and then register via the app. You, however, seem to have downloaded the app and then just registered directly via the web (nothing wrong with that, just unusual).
os is 10.9.5. I registered on line as the app didn’t open. Installed fully with licence agreement etc, but if you click on it it doesn’t open. Not aware I am blocking internet access, though this shouldn’t stop it opening. The icon is there but clicking on it doesn’t do anything. Do I need newer MacOS?
Can you check the contents of the following folder: ~/.local/share/AxCrypt and send the text-files you find there to our email support (support att axcrypt dott net). You can also check the contents yourself, and see if it might give you an idea. If AxCrypt starts but crashes, there should be some crash information there.