Winston has an inner conflict with Julia's person. She is a good lover, and a conversationalist, but she hard understands what he can because she is so young. Although she is up for rebellion, she does not understand the value of life with thought, one's own thought. Winston notices of her:
He felt her shoulders give a wriggle of dissent. She always contradicted him when he said anything of this kind. She would not accept it as a law of nature that the individual is always defeated.
Sure it was fun to escape together, but she didn't understand the permanence of the Party's change to society because she was a product of the Party. Sure, she rebels, but she does not need revolution. This conflict is going to threaten Winston's ability to maintain the relationship. He needs a partner in thought, not just deed. (This occurs in Book 2, chapter 3 when Winston and Julia's relationship is starting to flourish)
Another example of an internal conflict is much more straightforward. Winston recalls being a child and being demanding of his mother. He took off from the house after taking his chocolate ration and his return looked like this:
He never saw his mother again. After he had devoured the chocolate he felt somewhat ashamed of himself and hung about in the streets for several hours, until hunger drove him home. When he came back his mother had disappeared. This was already becoming normal at that time. Nothing was gone from the room except his mother and his sister. They had not taken any clothes, not even his mother's overcoat. To this day he did not know with any certainty that his mother was dead.
Winston is living with this responsibility. He feels ashamed that he did this and then upon his return, his mother was gone. Although so much of this story is told as a matter-of-fact, Winston references his mother every few chapters so he must have enough recollection of her that he feels bad about it. This occurs in Book 2, chapter 7.