power button defect: how do I turn my device on Recently my power button stopped working, meaning that it does not accept any input. With Cyanogenmod, it was easy to add easily accessible buttons in the notification area to turn the screen off.

However I fear the time when the phone is turned off some time in the future (maybe through 0% battery level). How do I turn the device on?

I hesitate opening the device (which I've done before) because of this very same situation. I'm not sure if the button is repairable, so I'd very much like to have a backup plan to turn it back on (since for opening the device, the battery must be removed).
If it's a hardware defect, I would suggest sending it to a service center for repair. You could plug it to a portable power bank so it lasts longer. But before you do that, you might want to back up your data to your PC or somewhere else first.