I purchased Diablo 3 without checking the requirements (I know, I'm dumb). I got it working, but it's insanely slow and barely playable. I give up and I won't be playing it. So I want to give my copy to a friend, but I assume they won't be able to install it without the authentication key, correct? Is there any way I can get a new key so my friend can install it on his machine?
Have you tried asking customer service? They don't have to do anything about it, but if you explain it doesn't play well for you, and you'd like to make your friend incredibly happy, they may do it for you anyway.
They do returns if you just don't like the game so maybe they'll do a transfer if it's unplayable.
No. Battle.net registration keys are single-use and are bound to your Battle.net account after you enter the key. If the registration key has been tied to your Battle.net account (if you were able to play the game, it was), it is not possible to un-assign or transfer that registration key. The only way for your friend to get their own registration key would be to buy a new copy of the game.