I've often wondered whether Hamlet would not have been very happy to have accepted his uncle as the new King of Denmark if that's where Claudius has stopped.

Hamlet is a scholar, and he apparently had a great time at Wittenberg. If he had been able to go back there and not be (perhaps never be) King, it may have been fine with him. Hamlet doesn't seem that much like his father, who is an active, soldierly sort much like Fortinbras appears to be. Hamlet doesn't seem all that ambitious to be king. (He seems determine that Claudius will not be, though.)

But it seems to me it's the marriage that is really sticking in his craw.