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