MobileMe rejecting password

Having read through the entire iCloud Rejecting Password thread, my situation is different only because it involves MobileMe/iCloud together.
I am running Snow Leopard 10.6.8 with a MM system pref pane that says. "Your MobileMe account has been upgraded to iCloud." I did this about a week ago.
Everything has been fine until this morning. I have changed nothing on the iMac. Mail app in the dock keeps giving me a dialog box titled Enter Password for Account MobileMe". The text of the dialog box says, "The MobileMe IMAP server “mail.me.com” rejected the password for user (user name here).
Enter your password again or cancel."

It gives me space to enter the p/w, which I do, then I click on the OK button. Within 2 minutes, the box pops back up with the same info.
I am sure the problem is on Apple's end. I can access my MM/iCloud mail account through the web, just not through the Mail app.

Strange.

Thanks for this info. I just changed it to @mac.com. I'll see what happens.

No help. I changed it to @mac.com in Mail>Preferences>Accounts, under the Account Information tab, in the User Name field.

Success!

I created a new account in Mail, called it iCloud to keep it separate from MobileMe, and used the settings you provided. It works! And the wife thinks I am a genius.
Thank you, Bear, for your time and effort in this.
Can't believe how much I depend on the Mail app, now that I've been without it for a few days.