Hamlet's inner conflict centers around whether or not he should enact revenge upon his father's murder, or not. Wrapped up in that conflict are questions about whether the ghost of his father was real or not, because if not, then he would be murdering his uncle all because an evil ghost prompted him to. Also, Hamlet wonders whether or not he is capable of murdering his uncle; he spends so much of his time worrying and fretting about it, and so little time actually doing anything that he gets mad at himself for inactivity. It takes Hamlet the entire course of the play to go from a man who is fearful and hesitant and wallowing about "in words" to a man who can stand up and declare, "the readiness is all."
Before he learns of his uncle's betrayal and murder of his father, Hamlet's inner turmoil was caused by his distaste of his mother's actions in marrying so soon after becoming a widow. This conflict within him makes him so upset that he declares Denmark and everything in it "rotten" and vile. He is grieving for his father while at the same time seething over his mother's quick recovery and marriage. Once his father's ghost visits him, that conflict soon turns towards his own struggle to enact revenge. I hope those thoughts helped; good luck!