Sophia here from Shopify. Welcome to the Shopify Community!
I'm so sorry to hear that you've had a tough time adding a payment method and getting in touch with Shopify Support. You can email our team directly through the Shopify Help Center. Logging in here first speeds up the authentication process. However, I'm happy to send you an email if you haven't yet been in touch with our team.
Was there a particular error message coming up for each card you tried to add?