What does ''Kono watashi ga'' mean?


I've heard this in an anime but need to understand the definition of it




Since there isn't enough context to judge exactly in what sense it is used, I
guess it was similar to この私が〜します. And I also assume that you wonder why there
is この before 私.  
Here, "Kono watashi ga (この私が)" basically means "I", but it is emphasized. It
is also pronounced as "Kono watakushi ga" in more formal way.  
  
Ex:

  * もう20歳若ければ、この私が彼女と結婚している:   
If I was 20 years younger, I'd marry her myself. (Here, not others but I get
married to her)

  * 驚いたでしょうね、この私が延期してやろうと思うなんて:   
You are surprised at my wishing to postpone it.

  * よかったら、この私がそれを取ってきてあげましょうか?:   
If it is OK, shall I go get it?

