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?
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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.