Julie here from Shopify Support.
If you are having difficulties using your credit card to pay your Shopify bill, then it sounds like you may not be using a compatible payment method. Our help doc on payment methods for your Shopify bills outlines the payment methods that we accept.
Our billing system requires either a Visa, Mastercard, or AMEX card type. It must also be a full credit card (virtual credit cards, prepaid credit cards, and most hybrid credit/debit cards are not supported) and capable of accepting recurring charges.
It's worth noting that some credit/debit cards work in some cases, but they are not supported so may stop working at any time. This is a bank issue to do with the way that credit/debit transactions are processed, rather than an issue with our billing system. If you used a credit/debit card with your other store, then this would explain why you are having issues using it on your new store.
I hope this clears things up, but please feel free to let me know which card type you're trying to use. It would also be useful if you can share any specific error messages you're encountering, as that can help rule out any local issues.
Looking forward to your response!