I also had this problem where I had a credit card saved and it would not let me change it. I finally logged into https://accounts.intuit.com/index.html - and was able to change it there, so that when I paid for state return, it pre-populated it, and after I entered the security code on the card, the Continue button lit up. That is where the credit card info is saved. Using that URL, you can either create an account if you don't have one, or update your account info for Turbotax. Hope this helps.
