In particular, I'm wondering what happens when the card is used without a valid target for stopping or unstopping a ship.
Notably, the condition of being "stopped" is a condition that only seems available on a player's own turn. We don't normally say my cards are stopped on your turn; it just isn't my turn, so they can't perform the kinds of actions that unstopped cards perform on a player's turn. (That is, this is not like "tapping" in Magic.)
So if I play What does God Need with a Starship on my own turn but have no ships in play, I don't think I can stop or unstop my opponent's ship, as I wouldn't think it wouldn't be a valid target to be either stopped or unstopped.
So if my opponent then attempts to pick the option of letting me stop or unstop any ship in play on my own turn when I have no ships in play, what would the result be?
My first thought is that the card "wiffs" for lack of a target, and returns to my hand.
Or is it just, since there is no target for stopping or unstopping the ship, she or he must choose the other alternative of letting me download a ship. (I missed when this card wasn't banned yet, and could imagine that this would be a good reason for banning it in the first place, when there was no once per game limit.)
Or is it that I get to unstop my opponent's ship that she or he then can't use because it's not her or his turn?
Or does the card just go to my discard pile with no effect at all?