I have the same problem. I'm able to receive e-mails on my mobileme account but I can't send them (on my loptop). I can receive them and send them using the mobile.me (already migrated to icloud) site and though my iphone.
If mobileme was gone I don't think the other channels wouldn't work either, right?
And Roger, I wish I could try your solutions I am not able to try it becuase I'm not logged in and when I try I'm getting that error message.
What is weird, that same password works everywhere else.....
Does anyone else know what is going on?