I am sorry but I feel confused by "computer screen" and "computer" alone when I tried to tell my friends what I was doing.
(1): I am sitting in front of a computer screen talking to you with a webcam.
(2): I am sitting in front of a computer talking to you with a webcam.
I am not sure whether (1) and (2) are equivalent, but if they are, then, they will make me confused again:
when your computer becomes old and you are going to buy a new one, so how will you tell your parents about this then?
(1): Hi, Dad and Mom, I need some money to buy a new computer.
(2): Hi, Dad and Mom, I need some money to buy a new computer screen.