Hi Emily -
I figured out my issue, it was a little tricky. I had to re-enter the password in the Mail->Mail Preferences window for the account I was trying to change (we have two iCloud accounts). The window showed a password filled in already (the little dots), but apparently it is not the real password.
Hi there -
Thanks for the suggestions. My mail issues actually became more complicated when iCloud started deleting contacts from my address book. I ended up spending several hours at the Genius Bar, and we figured out that it was caused by a multitude of issues - one of which was corrupt user preferences. I had to delete my user account (Mac OS user account, that is) and reconfigure email etc on my laptop. Now, everything is working. Thank goodness for backups!