I cannot sign up for Cryteks CryENGINE, at this site. When I click on the "sign up and download" button, nothing happens. I would ask this on their forums, but for that, you need an account.
How do I sign up and download CryENGINE?
In my previous experience, the CryENGINE sign up page has its flaws. In summary of this example, the best solution you have is to try accessing the site from a different web browser.
Further matters of housekeeping may improve your usability:
If all matters fail, I have since found means to contact Crytek without having an actual account. You can email Crytek in regard to CryENGINE issues at email@example.com.