Hello,
There are a number of errors in the console of your checkout page http://prntscr.com/t0awdo and some of them are related to third-party plugins. We can’t check your Dashboard because of permissions http://prntscr.com/t0axes
So, try to disable third-party plugins that you use and check checkout again. If the problem still persists after that, please, unblock access to your WP Dashboard and also provide us with access to your FTP to check the issue in more detail.
Regards