If it's a paid service, there's a good chance that you've been blocked cause your device has never been registered.
You'll have to contact the service provider directly.
On second thought, there's a chance that the public wi-fi is simply just a bunch of crap like how my school used to be.
In that case, you can try typing the IP to the wi-fi beacon directly.
In my case, it was the regular 192.168.1.1, which will redirect me to the official login page where I could input my student ID and password.