CharlesGrey: Hah, take that, nay-sayers! Looks like GOG support did a fine job once again.
Good to hear you have your account back. And if you lost any gift codes or anything like that, support can probably sort that out for you, as well. Any idea yet, why this happened?
Fesin: Doesn't look like they went for the gift codes. Maybe they were too cheap for them. :p
No, honestly no idea, still trying to figure it out.
Another strange thing that happened, is that all the e-mails from the account that I've been using for GOG.com disappeared, even though it seems like the e-mail account itself was secure (I was able to log in and change the password). No idea what's going on there, but it's kinda strange.
Might be related to your mail account then. Either that, or you do have some sort of trojan on your PC, and various accounts/passwords of yours have been compromised. Very frustrating, either way. :/
Do keep us updated in case you figure out the source of the problem, since it might help others.
Edit: Might want to change any important passwords, just in case, and don't use the potentially compromised computer for now.