Can't verify Apple ID because my email is no longer valid

I have an old Ipod and it's been working fine for years. Recently it stopped connecting to wifi and I've come to understand it's because it needs me to verify my Apple ID. The problem is, the ID for that device is linked to an email address that no longer exists (we switched from Bell to Gmail and now can't access the old Bell email.)

I can't remember the password because it's been so long since we've had to use it and am not able to do the "forgot password" thing because it will send the reset link to my old, unaccessable, email. I can't be the only one to experience this and don't want to throw away an Ipod I paid over $300 for because of this.

How can I verify my Apple ID in a situation like this? Thanks