Chosen Solution

My Mac Book Air (2013) has a broken Power Button. There‘s no function if I try to turn it on or off with Power Button. But if I disconnect my battery and connect it again, it‘ll turning on. So is this a keyboard issue and will be solved with a new one? Can it be caused to my battery? Or is there another potential reason? Thanks :)

It does sound like you narrowed down the issue. There is a set of contacts (power pads) on the logic board which if you short across them for a moment your should also power on.

If they do then you’ll need a new uppercase (which is the easier fix) or you need to replace the keyboard its self (much harder) for either you’ll need to follow this guide: MacBook Air 11" Mid 2011 Upper Case Replacement Finding the upper case part will take a bit of hunting as they are no longer being made look for Apple P/N 661-6072