Erase All Contents and Settings
How do I Erase All Contents and Settings on iPhone 4 (8GB) an old phone?
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When prompted with Apple ID password Verification fails.
Email changed and so did carrier.
iPhone 4 (8GB)
Carrier should not matter at all and email should update with any changes as long as the iPhone can connect to the Internet. Maybe try erasing with a computer.
See these support articles:
Restore your iPhone, iPad, or iPod to factory settings [with a computer] - "A factory restore erases the information and settings on your iPhone, iPad, or iPod and installs the latest version of iOS or iPod software."
Click here --> http://support.apple.com/HT201252
How to erase your iPhone, iPad, or iPod touch
"Learn how to wipe information from your iPhone, iPad, or iPod touch and restore your device to factory settings." Without using a computer. Does not reinstall iOS.
Click here --> https://support.apple.com/HT201274
If neither of the above work, read the "If you can't erase your device" section in the last link, including the last part about contacting Apple.