What to do, if SG support don't respond?

It means that the user, for some reason, unmarked the giveaway from received. First check if the user activated the game to their account, then add them to ask them why they didn't mark as received or if there's anything wrong with the activation (if they didn't activate it).

As for support, it may take up to a few weeks before getting a response.

Support is quite busy with tons of support tickets, the only thing to do is wait ^^

As far as I know, the support guys do see new tickets first, so try closing your current ticket and create a new one.

What Pesmerga said + don't bump your ticket cos it puts it at the end of the queue.

What to do, if SG support don't respond?

wait more.

btw, what kind of ticket did you send, Request Received Feedback?

Try to contact the winner first, it's all in their interest to mark giveaways correctly, as "misuse of giveaway feedback" is punished with permanent suspension.
There's a chance it might've been a genuine mistake on their part, but if it wasn't and they don't collaborate, you'll need to provide support with proof that you sent a working key, and they received it.
Then, you'll need to wait, as forced feedback can only be done by Mods and up, which basically means a grand total of three guys right now.