What happens if I start a giveaway with a key that is already redeemed?

The person trying to activate the key will get a "duplicate key" message and won't be able to activate the game and will mark it as not received, which limits the amount of GAs you can make. It's also not looked kindly upon by the community.

Edit: Removed bad advice :p

You are going to get a "not received" feedback.

It's best to put those in the orphan key thread
You can also use keygiveaway.com and put the link to your giveaway in the above mentioned thread.

Whoever wins the already redeemed key can (and probably will) badger you for a valid copy of the game for a week, and after that mark as "not received" unless you can get him a legit copy.

So if you know how many keys you've already used, one plan is to not give away more of them than you know should still work. And then work with winners to find out which ones have already been used and which ones haven't.