Mid 2012 Airs-- Not really affected by board issues that would effect booting. I have seen solid state drives fail in these. It is also possible that your trackpad and keyboard have and issue and are preventing boot.
Unless of course it is not powering on. Then we may have a board issue going on. Do you hear a chime when it starts or is it stone dead? In the case of it being stone dead, it is probably a board issue..
Hanging halfway though boot with the ability to force shut it off by holding the power button = SSD
Hanging halfway through boot with no ability to force shut it off = probably keyboard /trackpad / flex cable
Not powering on and no chime = board issue. In the case of this laptop given it's age my guess would be the ISL chip that handles battery charging and generates the main power rail of the computer. Simple chip to replace if you find someone with the proper skillset.