How has Claudius been affected in or by Act 4?
By the end of Act III, Claudius has revealed that he perceives Hamlet as a major threat. As he tells Rosencrantz and Guildenstern, whose duplicity by this point is beyond doubt, he is fed up with his stepson:
I like him not, nor stands it safe with us
To let his madness range.
The turning point for Claudius, of course, was the play staged by Hamlet. Claudius's reaction to the play leaves no doubt of his guilt, and he knows that Hamlet is aware that he murdered the former king. Yet we also learn, in a powerful soliloquy, that Claudius is tormented by guilt for his actions:
O, my offence is rank, it smells to heaven;
It hath the primal eldest curse upon't,
A brother's murder!
As he kneels in prayer, with Hamlet secretly watching, he realizes that he will not be forgiven for the dreadful sin he has committed. Moreover, by Act IV, he has learned that Hamlet has killed Polonius. It is at this point that we learn that Claudius, having already decided to send Hamlet to England, does not wish him to return. Indeed, he demands that the English execute Hamlet:
Do it, England;
For like the hectic in my blood he rages,
And thou must cure me. Till I know 'tis done,
Howe'er my haps, my joys were ne'er begun.
Claudius now knows that Hamlet will be his undoing, and he is obsessed with destroying him. If he was semi-contrite (although well aware of the threat Hamlet poses) at the end of Act III, by Act IV he is determined to consolidate his power by ridding himself of his stepson.