My first BNW game is with Assyria on King. My war machine has been rolling over cities from the beginning and I'm ahead in tech, but I've been slowed down significantly due to diplomacy, happiness and gold problems. I can't trade because everyone hates me, nor can I set up good trade routes, even to CS's, because everyone is always declaring war on me. I'm only in the mid-game (just started using cannons) and have been at war with most civs multiple times, including currently, where every Civ left in the game (6 or 7) is simultaneously at war with me, and I'm on Pangea, having started in the middle of the map. I dipped as far low into happiness as -28 (I've killed 8 rebel units thus far, but they've been good at pillaging my luxuries). I've spent many turns in negative gold as well, since I have no trade but need my large army. Being at war with everyone has also put me into defense-mode and obviously has stopped my expansion. And although I hosted the world congress, everyone has been ganging up on me there as well .
I obviously didn't play great so far, but I can still win since I am (slightly) ahead in production and tech, and I have high XP military units. Despite being at war on three fronts, I'm surviving the onslaught and currently am just about ready to get back into offensive mode and to start capturing more cities. I'm hoping that as the other Civs expand they start warring with each other instead of focusing on me, which should buy me enough time to get a domination victory before one of them gets a cultural or diplomatic victory.