It does not matter that the old email is no longer functioning. Use
the link providedhttps://iforgot.apple.com/password/verify/appleid
to reset the password, log in to iCloud and do the following:
Prepare your device to sell or give away
Even if you are sure you have done all those things, do them again slowly
and in the order given.
Then you should be able to setup the iPhone as new using your new
AppleID. Be advised all media/apps/music/etc downloaded with the
old AppleID is forever tied to that ID. You cannot transfer items from one
AppleID to another nor can you merge AppleIDs. Any items paid for under
the old AppleID will have to be purchased again under the new AppleID.
If all you wanted to do was change the email associated with your Apple ID,
it is not necessary to make a new Apple ID. You can make desired changes
by using this link:
https://www.apple.com/support/appleid/manage/