Victor, you present a compelling argument, which I definitely enjoyed reading. Still, I will argue against your conclusion. That said, my point is not to prove that I am right (which remains debatable), but to promote a wide discussion that sheds further light on the issue. By analogy, I absolutely hate to see true-false questions on exams, such as “True or false: A virus is alive.” I would much rather see an exam question that says “Present a strong case for or against the following assertion: A virus is alive.”
So here is where I disagree with your conclusion. In your model, the viral DNA (or RNA) is a living entity within the host cell that it has invaded. However, in the original cell, before the virus invades, we consider the cell to be alive, not the DNA. As I see it, the viral DNA is simply a small addition to the cell. The cell remains alive after the invasion, but no single component of the cell can be said to be alive, in my view. Even if you concede my assertion, you could still argue against me by saying that the entire host cell can now be considered a living virus. I would disagree with that, but there is some merit to the argument.