Mail not working/passwords not working/inbox frozen cannot use

New Mac Book Pro four of my mac.com addresses not collecting mail. The online button to the right of the address does not work. Apple told me it's best to only have one mac.com address. That is no solution after two hours on the phone. How can I collect mail again in these four boxes. I tried changing passwords and that did not work. Plus Apple had me delete one box, unable to add it back, keeps telling me I already own that address.????? Ready to send this computer back.