The first thing you need to do is to clarify the model of your Mac. Your TAG line says that you have a "MacBook Air, Model A1534." However an, "A1534," is a 12" Retina MacBook, not a MacBook Air. Click on the Apple menu's, "About This Mac," to determine the exact model of your Mac.
When you provide inaccurate, conflicting information, it makes it difficult to provide specific information about your issue, i.e., MacBook Air's may have removable SSDs, 12" Retina MacBook's don't.
Kappy is correct, simply moving the logic board from one Mac to another isn't going to magically repair the logic board.