when you try and sign in and keep getting verification failed

Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone, iPad, or iPod touch         

Try a forced restart.

Reset Device.      

If necessary

Hard reset.        

Do a backup and try a factory reset. Then restore from your backup.

Restore to Factory setting.      

Backup - Restore your device from an iCloud or iTunes backup.      

See these reads. I cannot guarantee a solution though.

Verification failed https://discussions.apple.com/thread/8321958

Apple ID Verification Failed: Unknown Error Occurred https://discussions.apple.com/thread/8343214

hthttps://discussions.apple.com/thread/72383

Verification failed : There was an error connecting to apple id server https://discussions.apple.com/thread/7238348

Error Connecting Apple ID, Verification Failed. How-To Fix https://appletoolbox.com/error-connecting-apple-id-verification-failed-how-to-fix/

How To Fix Verification Failed Error Prompt After Update To iOS 13 https://www.ikream.com/how-to-fix-verification-failed-error-prompt-after-update-to-ios-13-36692

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And see If you get an error when trying to activate iMessage or FaceTime https://support.apple.com/en-us/HT201422Especially see the contact options in the document.