iPhone 13 not turning on

If you're sure you used these correct instructions: Put it on charge for at least half an hour, then, keeping it plugged in, use these gestures:

Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the side (power) button. Only when the Apple logo appears (it might take 10-20 seconds), release that button (ignore all other screens that might appear, the one with the "slider" to turn the device off included).

If you can, check your battery status in Settings>Battery>Battery Health & Charging>Maximum capacity. If it is close to 83-80%, have it replaced as soon as possible, since it might have unpredictable behavior.

If the issue still 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:--> https://locate.apple.com/choose-country-region . 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.

Make sure that your device has the latest version of iOS or iPadOS and that your apps are up to date.

Please follow the steps in the following link for support with this issue: If your iOS device restarts or displays the Apple logo or a spinning gear unexpectedly