http://www.gog.com/support/website_help/shopping_experience First up, you stated that the card was revealed to have stolen information as of this morning. The GOG server uses a secure network akin to any other major online supplier. The only information retained from the cards is the barest minimum in order to confirm a transaction and verify the card information, which in itself isn't enough to allow someone access.
Second, the information didn't actually go through. Chances are the information was killed as soon as verification showed it couldn't be used. We're looking at 2 situations here where a card could possibly have been stolen: First is that the servers have been bypassed, allowing theft of your information before the data was encrypted and verified. However, anyone who could do that with a smaller website like this would have so much more financial gain on a website such as Amazon.com or Google. The second possibility is that your computer has a targeted rootkit or virus that either took data of your keystrokes, or pictures, and sent it outside to another person to be used. This would also be difficult to verify however, and if was the case, your prepaid cards are going to be empty too.
Third, this is a situation where you say knowledge of the theft occurred over a single day. That is VERY unlikely that it took a single day to discover fraudulent activity, and probably came from anywhere of several weeks to a month or more before any activity actually happened where your data was compromised. Your best bet is to check with your card company and dispute any charges you didn't make yourself, and they will almost certainly refund most of the money, and replace your card.
Other than all that we can't say much that can possibly help you other than to try and consider all opportunities instead of the one directly in front of you.