MacBook air won't startup unless power button held on for long time.

Your system is going into an SMC latched condition! Let's get some better diagnostics of your problem as it could be a few different issues!

First install this gem of an app! CoconutBattery take a snapshot of the apps main window and post it here for us to see 기존 질문에 이미지 추가하기 as often the batteries get long in the tooth.

Second, I would run the onboard diagnostics to see if a firm error code is generated. If it does let us know what it is. To enter into diagnostics restart your system and press the D key to enter!

Reference: Mac startup key combinations