This is a separate thing from the subject, but I agree with you. I've discussed this idea at length with a friend of mine. The way I see it, once your brain is dead, you're dead, no matter how awesome the copy you made is. A fictional transporter illustrates it well, I think.
Let's say there's a transporter device which destroys your physical body, and sends it's information to a sister machine, which assembles an exact duplicate.
Let's say there's a problem with the first machine, and it does not destroy your original body, yet the copy is still made. Obviously, the copy is not you, since you're still fully alive, fully functional, at your start point.
The same is true for putting your mind in a computer, or something like it. Unless it's a direct link and life support system for your brain, how does your mind actually enter the machine? After all, your mind is the effect of your brain functions. Even if you made a program which exactly duplicated your thoughts, it's still not you.