No the Only Once! plug-in does not block users during registration. It only blocks users that are trying to log into the Joomla! site twice, with the same user credentials (username/password) and thus having two sessions active at the same time, regardless which work station they are using.
I gather that with "they must not be able to register or log-in again BY A DIFFERENT EMAIL ADDRESSE OR USER NAME", you mean they should not qualify for another 14 days trial membership?
Again, my plugin doesn't do that.
What you may be looking for, is a registration - in your website's database - of the IP-address for which a trial membership has been granted, followed by blocking all future requests for the same trial membership from the same IP-address (with an option to unblock it by your admin, I would suggest).
I don't know if there is a module/plug-in available that can do this, but it can be made. The bad news is, if you want me to build one for you, I will need to charge a fee...
If you're interested, please email me on This email address is being protected from spambots. You need JavaScript enabled to view it.