In scene 2, Claudius addresses Hamlet a number of times, but Hamlet answers him only once. How does hamlet clearly snub his uncle, the new king?
In Shakespeare's Hamlet, Act 1:2 (I'm assuming this is the scene you're referring to, since you don't mention which act), Hamlet does technically only respond specifically to Claudius one time, but Claudius is there when Hamlet responds to his mother. They are all three involved in a short conversation. Hamlet ridicules Claudius, but I don't think it's done by his not answering Claudius, it's done by the answers he uses.
And, in fact, Claudius addresses Hamlet one less time than you think. The aside that occurs at line 65 of the scene is spoken by Hamlet to the audience, when Claudius pauses. Claudius is addressing Hamlet here, but he is not finished with his thought when Hamlet gives the aside. Notice the dash at the end of line 64. Claudius's complete thought would read like this:
But now, my cousin Hamlet, and my son--
How is it that the clouds still hang on you?
That's one address by Claudius to Hamlet, with Hamlet's aside coming in between the greeting and the question.
And, again, when Hamlet answers Gertrude, Claudius is there and is part of the conversation. It's the answers, not snubbing, that ridicule Claudius. But the answers are for another question.