Wow......That is expensive......Your logicboard is where your processor - graphics card - controller are installed in.
It's not worth paying that much for a logicboard.
Check powerbookmedic.com and look up your macbook pro's model there and see if you can get it cheaper.
From there - go to ifixit.com and get the instructions/guide on how to replace your logicboard.
It will be cheaper than the one Apple quoted you.
For that price however, I'd buy a new 13 Inch Macbook Pro or 13 Inch Macbook Air.
Good luck - hope you get it sorted out.