Same thing happened to me. Card got expired but they wouldn't let us add a new card (or payment method as they call it) because the account was in some invalid state. When asked what it was, they couldn't give the details due to legal reasons.

It took about 2 months with support (Business support) and finally they chose to close the account.

We created a new account with a new card and migrated our AWS infrastructure. Unfortunately we still have to use AWS..for now.