Take the phone to a shop (even a TV repair shop) and ask them to measure the battery voltage for you. It should be around 3..6-3.8 Volts. If it's really lower than that (I've rejuvenated batteries that were down to 2.4 Volts - which is about -200% if you follow the calibration curve down below 0%), you'll need a cellphone shop that can recharge it for you or a new battery (look on Amazon - Anker or Hyperion should have one for your phone for about $15 or less).
If the battery is charged, taking it out will turn the phone off. (Hold the power button in for 5 seconds to drain off any remaining charge.) Put the battery back in, press the power button, and the phone should turn on. If it doesn't, it needs to be repaired.