So... when you click on the blue Register button using the email test@test.com, then nothing happens at all.
Is this what happens for other people when they try to register? You mentioned that six people were able to register successfully, but past that, nobody has been able to register. So, how many people after the original six tried to register? And did they report that the same exact thing happens to them? They hit Register and then nothing happens? They don't get any kind of error message?
I'm also wondering--in your screenshot, it showed the Safari browser. Can you try to use the registration link and register with a new email address in a different browser (Chrome or Firefox, for instance), and see if it has the same behavior?