Hi Stephanie
The problem is definitely with your power button. With the type of failure you’re having I’m guess some type of water damage. Luckily this phone isn’t too hard to work on and the power button is a cheap replacement. I would recommend going for it!
If you find any water damage (white corrosion) inside, you should scrub it gently with some alcohol and a toothbrush to clean it up.
Best of luck!