Can't use icloud after changing email and apple id

Recently my email account stopped working and I had to change to a new account. I changed to the new email address in my apple id, but now I can't get to Icloud because it's tied to my old email address. It's a frustrating circle, because Icloud wants the old address and password and when I try to set my id back to the old email address, I get an error message saying the email address is not valid.