The picture you show is the Restore Screen. If the information in the link does not help, then, as suggested at the end of the article, contact Apple Support.
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If you see the Restore screen on your iPhone, iPad, or iPod touch - https://support.apple.com/en-us/HT203122
Then for the serial number, Click on the link on the top of this page.
It won’t let me get to the recover screen at all
What can I do from here What if my iPod is scratched and can’t get serial number , also the iPod won’t work to get the serial number on phone