Can I replace the logic board in a 17" 2009 MacBook Pro with one from a 15" 2009 MacBook Pro? I've got a working 15" Mid 2009 MacBook Pro. I've found the same model MacBook Pro, but with a 17" LCD.

Can I replace from the 17" MacBook Pro with the logic board from my 15" MacBook Pro in order to get a larger screen size?
As far as I understand your question, you say that you have found a 17" 2009 MacBook Pro that has a working LCD panel, but not a working system. You already have a working 15" 2009 MacBook Pro, and you want to know if you can transfer the system board from the 15" MacBook Pro and connect it to the 17" LCD in order to get a working system with a larger screen size.

The answer is unfortunately no, that won't work. The 15" and 17" logic boards are vastly different, and will not support each other's displays.