Sorry to hear it. It's a week past the date to make changes, and very close to the drawing now (1/31/12 and 2/1/12) though I don't suppose there is harm in asking. The worst they can say is no.
If you used someone else's credit card, if there is a typo in your registration, if your expiration date isn't correct on your registration, your order will be declined. If you contact us before January 22nd we can assist you in re-registering. Go to this link and choose "other" and fill out the short form. Someone will get back to you as soon as possible: http://tickets2.burningman.com/contact.php
You might also try contacting Participant Services via partiserv(at)burningman(dot)com ASAP, though I think the form is the official way. If you send an email you might want to mention that you have also submitted the online form.
If the card actually gets run & declined during the drawings on 1/31 and 2/1, there won't be an opportunity to give a new number right at that time, as the selection process automatically skips declines and moves on to the next valid card.
There will be other chances--10,000 more tickets sold in March, as well as an online system to buy/sell and avoid Craigslist an eBay (details coming soon).
Good luck to you.