I have a solution!! I'll post it here because it's fairly simple.
As was alluded to earlier in this forum or other forums is that it's a MobileMe transition problem with the passwords, they aren't coding correctly or blah blah blah whatever it is that's wrong with it. It's not easy to change your iCloud password, so you have to go here:
https://appleid.apple.com/cgi-bin/WebObjects/MyAppleId.woa/
or appleid.apple.com and it redirects.
Sign into your account under "Manage my account" and reset your password to a new one, it can be similar just not the same as the current. Make sure it's your @me account and not your iTunes Apple ID (if they are separate).
Optional step to help reset everything: Sign out of iCloud through your System Preferences. It'll ask you to delete contacts, calendars etc. You should be able to delete everything because it's still backed up on the cloud. Do all that, delete the email account in Mail. Then sign back in and reinstate everything with the new password. Go to Mail and add a new iCloud account with the new password. Empty the Cache in Safari. Log back in via the website. Go to your iPhone settings and change the password under the iCloud setting (not Mail). That'll reset everything.
That should work to reset your password everywhere, resync all of your data and get you collecting your email again.
Pass it on.