Well, can't say for sure but I had a similar problem on all my macs. Apple Mail stopped receiving my emails and was constantly reporting my password was incorrect. In desperation, I decided to remove my iCloud account from my computer to add it again and got it fully working again (I did this a few hours ealier).
Note that I could login on icloud.com with my email/password.
I closed iCal, Apple Mail, Address book.
I went to System Preferences > iCloud > Sign out.
Removed contacts, calendars.
Then signed back in.
Then it should take a few seconds to get your calendars/contacts.
Your emails should still be in Apple Mail which, at least for me, started receiving them again.
It seems to me that this issue is related to a problem in the keychain.
Not sure why this fixed it for me so I can't garantee it will work for you.
Good luck!