what feature, site or service are you trying to change the password ***** or set up new account?
Ok and would you prefer to set up a new Apple ID or try to recover access to your old one?
(Keep in mind that any purchases previously made under the old ID are lost if you do not have access to that account.)
Are you still able to sign into your existing account?
test out that it is working properly by signing into the Apple ID management site:
https://appleid.apple.com/ (under "Manage Your Apple account")
When you try using your new email address, does it say it's already in use?
Ok and when you enter your email address what is the exact message it gives you?