How does a specific software recognize my computer?

Hi there, I need a solution to the following problem. I bought a computer from a friend of mine a couple of weeks ago and now I wanted to play at a specific online casino. So I downloaded the software and installed it. When the software client came up I entered my user details and clicked log in. Unfortunately an error message came up saying that the login failed because the maximum number of players registered on this machine was exceeded and I cannot play at the download casino. I contacted the support and they confirmed what the message stated. I asked them what I could do, but the support obviously had no clue as they do not create the actual software. I called my friend and he said he played at the same casino month ago and then uninstalled it. So I thought that I could clean the computer and tried a few things. I let a reg finder tool run over my computer to find any registry files from the software. I found some entries and I deleted them. I also tried to download it with a different IP address and then installed the software again. It didn´t work. Just to put it in the right frame: I want to play at this casino because it is the only one that offers a certain game. So I am not really a tech geek and I don´t know what I could do further. My question is: How can this specific software detect that is has already been downloaded and installed on this computer and more importantly and the main part of the job: how can I solve the problem without having to reinstall windows? Any help that leads to the solution will be appreciated and generously rewarded. Please also contact me via PM so we can discuss the details. Please only bid on this project if you are experienced with softwares or have worked on similar projects. Thanks for any help in advance! Best regards