Hi Patryk,
There is some other JavaScript on the page that is conflicting with the s2Member JavaScript, probably from another WordPress plugin or even from your WordPress theme.
In situations like these we recommend disabling plugins until you find the one causing the problem. If you don’t want to do that, you could also install the Plugin Organizer plugin, which allows you to selectively disable plugins for a specific page. You could disable all the plugins for your payment page and then see if that fixes the problem.