Phone is completely dead

See if it's a temporary glitch trying a "forced" restart of your device using these 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 the issue persists, it could be a hardware (battery? other internal component?) failure but we, just users like you, cannot diagnose that issue remotely, sorry.

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.

If your iPhone won't turn on or is frozen, try the things outlined in this support article --> If your iPhone won't turn on or is frozen - Apple Support

Sections about...

- If your screen is black or frozen

- If your device turns on but gets stuck during start up, try to update it.

- If your device still won't turn on or start up, contact Apple Support at https://getsupport.apple.com/?caller=kbase

Hi!

If your iPhone 13 does not turn on and looks "dead", you can try a forced reboot. To do so:

Quickly press and release the Volume Up button

Quickly press and release the Volume down button

Long press the side button (power) until the Apple logo appears

You have to try several times, be patient but especially fast. If you are not fast, forced reboot will not work.

If it didn’t work, try updating or restoring it from a computer. To do so:

•If you have a Mac running MacOS Catalina 10.15 or later: To update via Finder, open a Finder window and connect your iPhone to your computer. Select the device in the left sidebar of the Finder window and click General, then click Check for updates. Click Download and Update and follow the on-screen instructions.

To reset your iPhone via Finder, you should put your iPhone in recovery mode. To do this you need to connect your iPhone to your computer with a Lightning cable and quickly press and release the Volume Up, Volume Down and Side buttons until the recovery mode screen appears. Select your iPhone in the Finder window and choose to reset your iPhone.

•If you have a Mac running MacOS Mojave 10.14 or earlier or a Windows PC: To update your iPhone via iTunes, open iTunes on your computer and connect your iPhone to your computer. Click the device button in the iTunes toolbar, and in the Summary pane, click Check for Updates. Click Download and Update and follow the on-screen instructions.

To restore your iPhone via iTunes, open iTunes on your computer and connect your iPhone to your computer. Click the "Device" icon and go to the "Summary" window. Then press the "Restore iPhone" button

If the problem persists, contact Apple Support.

I hope I helped you!