Read this

With no errors in the logs it's difficult to say what might be wrong.

Have you really tested with ALL 3rd party plugins disabled to be sure that there's no problem in one of them? Is there also no error displayed in the browser console (development tools of browser)?

Have you modified any Elgg core files (any at all or more specifically a language file)? If you modified a core file and saved your changes in the wring encoding (with Byte Order Marks / BOMs) it might explain why you have a problem. BOMs are non-printable characters added at the beginning of the file that would cause problems. Likewise, if you added anything at the beginning of a file before <?php it would cause problems. So, save any files with encoding "utf9 without BOMs" if you make any modifications.

http://learn.elgg.org/en/stable/guides/authentication.html?highlight=pam#pluggable-authentication-modules

Yes, giving up is always the easiest solution.

I just don't have anymore time to invest into this project.

@anax-dev: I worked with stripe and stripe_subscriptions plugins recently for Elgg 2.3.x and made some changes in order to be compatible with latest stripe-php library.

They are available at https://github.com/nlybe/stripe_subscriptions and https://github.com/nlybe/stripe.