Macbook Air logic board upgrade
I think you're out of luck. From iFixit, here's the logic board from the original MacBook Air:



And here's the logic board from a 2012 MacBook Air:



Unlike desktops, which typically use standardized parts, laptops use fairly specialized components, and on top of that, Apple tends to iterate its designs fairly aggressively even within models with similar outwards appearance to achieve better cost or performance (e.g. smaller logic boards means more space for the battery). Because of this, most Apple components beyond hard drives and RAM are only interchangeable with those of the exact same generation.