In Act 1, John's main conflict is dealing with his lust for Abigail. He does still lust for her even though they ended the affair, but though she persists, he does not submit. She catches him alone and tries to tempt him but he remains strong. This was very hard for him, because it is so tempting and easy to submit. But he is very against hypocrites, and at first finds it hard to criticize the morality of others, making him feel hypocritical.
In Act 2, John is trying to deal with the consequences of his infidelity. Elizabeth won't trust him and he is deeply bothered by this. He is doing everything he can to prove his trustworthiness, and show her that he is trying to please her. He is also dealing with a lot of regret. He didn't want things to turn out like that between him and Elizabeth and now he feels like an inadequate husband. When he is angered so easily, it's frustration and self pity rearing their ugly heads. He realizes that he's hurt her but doesn't feel that he's done something unforgivable.
In Act 3, John's frustration is really starting to tire him out. He doesn't understand why Abby is pursuing him so, and feels responsible for Elizabeth's imprisonment. It is also very frustrating for him to feel powerless, and to not be trusted. He can usually remain even-headed, but when anger gets the best of him, he calls Abigail a whore. He was struggling with that truth, and had yet barely admitted it to himself when he blurted it out in court.
John's main internal conflict in Act 4 was definitely pride. He refused to admit to witchcraft, even though denial would mean hanging. He chose a proud name for his sons and...