Keep it. You're likely to sell it for quite a loss. If you think you're likely to find a partner again, you'll be in for buying one again. Diamonds are /forever/ (:P), keep and reuse it.
I'd argue that the lesson here is to choose the girl who doesn't need the engagement ring.
Don't you think it might be a bit awkward when your new partner learns where it came from?
I was once present for a very awkward conversation where a husband told us that his wife's ring was second hand in front of her and she was shocked. He thought she knew him well enough to know that he'd never buy one first hand...