My iPhone 12 with broken back won't turn on

Have you plugged it into power to charge? If you plug it in and it won't start on its own, then it is probably suffered internal damage or the battery has died. You can have Apple examine it for free, but any repair replacement will be charged. See this. Genius Bar Reservation and Apple Support Options - Apple

Do you have a question?

It's broken...

Make an appointment at the Genius Bar of your local Apple Store. It will probably have to be replaced.