Unforunately, what you are describing sounds similar to what others have experienced. You could always check with your card provider to make sure it wasn't charged, but I think the "declined" status is a pretty good indication that it wasn't.
To charge that original card now would take a "human" at Dreamhost to manually re-submit the charge with the (now) corrected code. At least you were able to get an "account" set up so you can reach support (even if it isn't "funded" yet).
It is my understanding, from other posts in this forum, that you will continue to get that error until someone at Dreamhost intervenes. You might try waiting a while (at least an hour or so - parts of the Dreamhost panel updates systems with processes that run periodically) and then either try the sign-up process again or, since you already have an "account", try adding that card via the Billing section of the control panel. If you are able to add the card to the control panel, you could probably create the hosting plan from within the panel.
I have no idea if that will work, but I can't see that it could hurt, as you are just waiting for a response from Dreamhost anyway...if it doesn't work, nothing is lost as you will still need to communicate with support to get it resolved.
Of course, these are just suggestions and YMMV - my sense of it from watching other posts about the "card is already in our system" situations is that it may take support to sort it.