Samsung Galaxy III won't turn on - power button seems broken

A

AC Question

My power button was acting fidgety all day - I kept getting the power off/restart screen without pushing the power button. I think it was getting stuck.
My phone just died of low battery but kept giving a short buzz every 2 or 3 seconds or so. I plugged it in and it kept buzzing. I can tell the battery is charging, but it is still buzzing but won't turn on. I wiggled the power button and it stopped buzzing for a short time but the next time I touched my phone the buzzing continued and it still won't turn on. Does anyone know what I can do to get the phone to turn on?