Hello miglena50,
Apple Service Programs are available at the very bottom of Apple.com/Support - they make it very clear whenever their is an available program.
I believe the one you are referencing is this one and you can enter your serial number here to see if your device is included: iPhone 11 Display Module Replacement Program for Touch Issues - Apple Support
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However, if your device is just unresponsive, have you tried to Force Restart it?
This is done with a combination of button presses and does not rely on the screen at all.
-> Force restart iPhone - Apple Support
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If that does not work, you can reach out to Apple Support using the following contact information to determine next steps:
Contact Apple Support:
| Call Apple Support 1-800-APL-CARE
| For International Numbers or ASL support, click here:
| Contact Apple for support and service - Apple Support
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| Chat with Apple Support
| Apple Support
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| Get Started Online
| Apple Support