Let's access your account via an incognito window to see if it's a browser-related issue or not. Let me walk you through how.
CTRL+SHIFT+N for Chrome.
CTRL+SHIFT+P for Internet Explorer and Mozilla Firefox.
After that, go back to selecting your payment method again. If it's working fine, you can to your regular browsing mode and clear its cache. This process will delete the temporary data stored in your browser.
Accessing your account using a different browser can be an option, too.