If it's happening with both the Mail application, and on the web through iCloud, my guess is it's nothing wrong with your computer. Something is either fubar in your mail account at Apple, or you're brain farting the password.
The error messages in your other post, where did those come from. Was that the message from the Mail app, or was that what the webpage displayed when you tried to go to your mail in iCloud.
It happens with both, the 'Mail' app and on the web. I got part of the 'error' message from the web page. I don't think I've had a brain fart because I never have to type in my password when opening the Mail app. And I've received e-mail just fine until yesterday afternoon.
The computer was off for the past few days. I hardly use it anymore and get my e-mail on the iPad where I repeatedly get this 'incorrect username or password' message. Again, I have it set up where I don't have to type in my password every time.
I don't get it........