I was listening to Professor Leighton Flowers talk about "responsibility," (mp3 - around 29 minutes into the debate) and he noticed that he tried to define it as "able to respond," as in being able to respond positively to God's commands and exhortations. That definition is just fanciful.
The term "responsible" actually means "answerable" or "accountable" - in other words, it's about the fact that the person is going to have to answer or respond for what he does. It means that the person will have to face the consequences of his actions. When we say that man is "responsible," we're not talking about some hypothetical philosophical ability to do something, but instead we're talking about the fact that man will have to give an account for all his actions before the Judge of All the Earth on judgment day.
Inability to do what is right is consistent with responsibility for doing what is wrong, because "responsibility" doesn't imply some very specific kind of hypothetical philosophical ability to have done otherwise, but rather it implies that the person will be punished for his sins - unless the person has a penal substitute in the person of Jesus Christ.