Unable to setup Mail using iCloud or directly in Mail Preferences

Not sure whether this is an iCloud, Mail, or Mountain Lion issue. I have cross-posted in the OS X area.

My Mail functionality has been degrading slowly but steadily over the past week. Today it became non-functional. Nothing in or out. Cannot connect to the iCloud server. The iCloud server status online shows there are no problems. I am doubtful of that.

But, I have looked at several similar requests and tried various things without success. So deleted the account (after backing up) with intention to start anew. I cannot get the IMAP setup to connect (Account Type: IMAP \\// Server: imap.mail.me.com); same problem -- iCloud server not available. I am also unable to setup using System Preferences as it refers me to Mail directly. I have full internet functionality in all other areas without difficulties.

Yes, I am able to login to iCloud.com, but definitely inconvenient.

Does anyone have any ideas? Am I missing something or this a genuine iCloud server access problem?

Thanks in advance.