Hi,
First, you will need to confirm the coverage status of your device. This will provide you accurate service pricing, and available service options.
Go to checkcoverage.apple.com and enter your serial number to confirm the coverage status. If you are able to navigate to the Settings app on that device despite the damage, you can also check your coverage status in Settings > General > About > Coverage.
If you have AppleCare+, AppleCare+ Theft & Loss, AppleCare Services, OR the device is Out of Warranty (Coverage Expired), see iPhone Repair & Service for estimated pricing based on the type of damage the device has. After confirming the device model and the type of service needed, you will see estimated pricing for service with AC+ coverage, as well as if the device is OOW. If you want to proceed with service, you can use getsupport.apple.com, the Apple Support app, or contact Apple Support.
If you see Coverage Expired, this means your device is out of warranty. It does not necessarily mean you do not have coverage. If you set up mobile protection insurance with your carrier that is completely separate and unrelated to AppleCare+ coverage, you would be eligible for service through your carriers partner insurance provider. These coverage types would never appear in Settings or online due to it being a third-party provided insurance for the affected device. If this is the case for you, contact your carrier.
I do not see anything in your original question regarding theft and/or loss of the device, but if that is the case, please clarify and i will provide those resources for you as well.
Hope this helps.
