I think the solilquy to which you are refering is in Act 3 scene 3 where Claudius expresses his guilt at killing his own brother. FOr me, this scene supports what I think of Claudius. Claudius is selfish, he is selfish throughout the whole play, and he is selfish in his guilt. In his solilquy, he's not worrying about anything other than himself, and the fact that he won't be forgiven in death for killing his brother. Cladius may feel the need to repent, but not for any other reason than he wants to get into heaven. Cladius is also a coward. He knows that Hamlet wants to kill him, and rather than confront him, he tries to pray that Hamlet will not hurt him. He was a coward before his siloquy, and the solilquy only emphasised that characteristic.