Try closing TurboTax, clear your Cache and Cookies if you are using TurboTax Online, and reopen TurboTax. You can also try a different browser.
Also, make sure you have ran all updates.
If using TurboTax Online: Clear your cache and cookies. See this FAQ, for your particular browser.
If using TurboTax Desktop: Please see this FAQ.
The FAQ link for the desktop version took me to how to install Turbo Tax. Is there something I need to do to get it to accept my credit card for the state filing fee?
Are you able to enter your information and it get's stuck or what do you mean by the program freezes?
When I select Pay by Credit Card, I get a pop up error. "Hmmm... we seem to be having trouble..." At that point, the program freezes and I can only close it through Task Manager.
Call Customer Service and tell them you have a "block payment issues, possibly due to billing or an invalid license" and the agent should be able to help you. Here is how you reach customer service: Turbo Tax Customer Service