What happens if the phone won’t turn on

Yes, that might be a reason.

But it also can be frozen, or have a hardware failure. See this support article:--> If your iPhone won't turn on or is frozen - Apple Support

If the issue persists, I suggest that you make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> Apple – Location Selector. After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.