Inspired by the many good points made on cybernetic immortality. Here's my take:

The problem is that what constitutes a person may or may not, according to your opinion, be something that can be captured inside a computer.

If you lose an arm, you do not die. You adapt. Life is different without that arm, but you are still you.

If you lose a sense, like hearing, you do not die. You adapt. Life is different as a deaf person, but you are still you.

(what happens if you add things? Can anyone think of an example?)

The point is as follows: If the change is made gradually, and the mind of the person is able to cope, there is no intrinsic problem with having a mind with no body. There is no qualitative difference between losing a arm and losing your whole body. You adapt.

See achieving cybernetic immortality.

Now, what would a mind be like without a body? A once human consciousness would behave very differently if all the joys, pains, and drives of biological function were removed. Maybe the mind would have its own drives. Maybe it would create artificial ones.