So what happens if a week goes by and the winner doesn't respond?

If you go to the winner's Steamgifts-profile there's a direct link to their Steam-profile and you shouldn't have to search. You just have to log in Steam from your browser window and you can add him/her to your friend list directly from there.

Since it's a cd-key and you already sent it through e-mail, it's sort of risky to reroll the giveaway after that and might give you more problems, for example if the game was already activated by the original winner. I'd suggest waiting for one week and if you haven't gotten any feedback by then, request it from Support. Of course you still should try adding them on Steam.