I am not sure to have understood your question.
in particular, what do you mean by "gaind access to my IP address"? your IP address, while surfing the net, is "public" and can be seen by any sw your computer communicate to (e.g. when you connect to a site, the site see your IP and can log it, legally; when you chat e.g. with IRC, the clients see each other IP address, and so on); indeed the communication is possible because of the fact that your IP is assigned to your machine in that moment and is known, or data packets couldn't reach you.
if your computer exposes services (even though you don't know), it is legal to try to access them (well configured computers for desktop usage normally do not open ports for incoming connections).
sites, to prevent spams or some other illegal or not good (for the site) activities, can check if different users access from the same IP. if it happens so, they legitimately can think the same person is accessing the site with different usernames (e.g. to gain "points" or whatever).
however, you can say them about the fact that you access the site with a public internet cafe as others, so that it is normal that the same IP appears for different usernames / handles.
from their POV, they haven't done anything illegal