Never, your opponent plays Thiefs/Noble Brigands on you
Can you be indefinitely prevented from making $5 after a 4/3 opening that way, though, I wonder?
Well, obviously not with NB... since it can't steal Coppers, then no matter how bad your luck is, you'll eventually draw 5 Coppers; assuming that you actually buy Coppers given the chance.
With Thief, absolutely. Assume that your opponent plays 2 Thiefs every turn... should be possible if we assume that worst luck for you includes best luck for your opponent. He can trash down to Village + Thief + Thief. While your bad luck is still preventing you from hitting $5 even without the opponent hurting you, he has time to do that. So then you quickly get to a game state where you have nothing in your deck but 3x Estate.
Ok, now I'm wondering... in a board without any virtual money, could a player do such a thing, thus forcing a stalemate?