I was having the same issue for almost a week now. My phone is visibly in great condition (screen in tack, no cracks or scratches, etc.), but the power button just gave out on me. The only time I was able to use it was if I plugged it into the battery.
Finally, i decided to download an app by searching "Power Button to Volume Button," and voilà it works. I now use my up or down volume to turn my phone on! I hope this helps you, too.