The meaning of "あなたがいるから"
"あなたがいるから"
This is the title of a song (sung by 横田はるな and 中島美嘉). My first impression is that it carries the meaning "Because you are here/around/present"... Is that a correct interpretation of the title?

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THT your guessing is correct, the answer Cyaoeu`s is correct too and nice translation.

you got perfect solution and there no explain for this answer, so i will give you phrase insted.
あなたがいるから、がんばれる。: i can do this because of you.
"あなたがいるから"
あなた giving it energy, whatever the willing to her career, things make want she do to him/her, giving her life meaningful, etc,.
 
another example when it is simple object. 
通れません、・・・・ 
あなたがいるから。
i think you understand this あなた no problem :D

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I would translate it as "because you're there", as in "you're there for me".

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anata ga iru means ,your there by my side