Injured Gadgets is (in my opinion) the best place for screens, batteries, and even other parts for both apple and android devices... here is a link for the iPhone 13 Screens and other parts: https://www.injuredgadgets.com/apple/iph...-13/

did you damage the board under the battery? did you short out any pins? hook up the battery? make sure everything looks like it should? no burnt parts? no torn cables? especially flat ribbon cables?