Had exact same issue, MBA (early 2015, A1466) does not switch on at all & charging light on the magsafe cable remains orange.
After trying everything including remove battery etc tried switching it on after removing the Trackbad/Keyboard cable (from any one side, either from the logic/mother board or from the trackpad side.
MBA boots up fine now and battery etc everything shows ok in about screen. FYI, it also boots up fine with external keyboard mouse connected over USB or bluetooth.
Probably need to replace either the keyboard or the touchpad ? (Though its strange that even fan wont turn on if kbd cable is attached)
Any way to know which one to replace - kbd or touchpad ? The keyboard cable connects to touchpad which in turn connects to the main board so i can eliminate them by connecting one by one.
Or maybe just the touchpad cable ? The moment i insert it into the zif connector system shuts off at once.
It seems instead of replacing keyboard its better to replace keyboard+top-cover; Is that correct ?