Can I replace the logic board with another model's logic board?

Hi there, I've got a macbook pro unibody 17 late 2011, and it's got a problem with its logic board.

when i try to turn it on, it beeps three times but a worker of third party repair shop told me that it's not a problem of ram but it's a problem of its logic board and required me about 700 GBP. However, as long as i am a student, i could not pay for it.

So, i was looking for some new/used logic board but it was really hard to find a logic board which fits on my laptop. but could find bunch of Early 2011's logic boards.

I want to ask if i can replace the logic board to 2011 early one or not.

thanks.