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I'm sorry, without seeing the screen you will not be able to unlock the screen and give permission to transfer the data. The computer or any other device will not see or read the phone unless you open the phone and give onscreen permission. What is the model of your phone? We can check if there any backup made online.
It is possible that your data are backed up online. So set up the new phone and while setting up, make sure you sign in to the same Google account and also the same Samsung account you used on the old phone. Does it ask you to restore from a backup?
Ignore the phone call offer. First, take out the SIM card from the old phone and put it on the new phone. Then setup the new phone by following the onscreen instructions. Skip the transfer from another/old phone option. Once you setup, open the Settings app on your new phone, choose Accouns and Backup > Backup and choose Restore option.
Make sure you sign in to the same Samsung or Google account you used on the old phone