Such errors cover a multitude of sins so unfortunately there is often no clear reason as to why it happens. However you mention it throws up the error immediately upon selecting credit card as the payment option but before you put in your card info, this seems to show that it's not your card actually at fault but a browser issue (even though you said you tried another browser, it's possible it's not the browser specifically but a security setting on your computer that is causing the trouble).

A common culprit is ad or script blocking aps or browser addons that interfere with a benign security script SE uses on that page to check your card details as legitimate - such aps have to be either disabled temporarily on that page or have the specific script whitelisted to allow the page to work without crashing with errors (as I understand it the security script name that needs whitelisting is 'gcsip').

Hopefully this hasn't been confusing, and helps.