Hi. What's the error after you enter your data. Are you logged into the Creative Cloud app under your registered user name?
Another suggestion would be to ensure there are no old vestiges of Illustrator on your computer. To do this, please use the Adobe Cleaner tool to completely uninstall old versions, log out of Creative Cloud, then restart your computer and log back in to the Creative Cloud app and try the download. If the error persists, please do include a screenshot of the error you're receiving.