"I then went into System Preferences for my Mac and selected iCloud (under Internet and Wireless) and then 'Manage' at the very bottom."
I tried something different: I entered my Apple ID and pressed Done; then opened the iCal, and found it worked perfectly/
The reason [in my case] is that I had just had to re-establish my identity - when Apple migrated accounts from @me.com to iCloud, it appears to have lost my details. So I could not log in, and my password was not recognised; and when I tried to work round that by answering my security questions it told me I had entered the wrong information for my own birthday!!
Googling 'find my apple ID' gave me a link to restore my identity, and provide a new password.
I believe this caused iCloud to have a spasm, and that stopped iCal, and my gmail account from working.
So - by clicking 'Manage' on iCloud in the System Preferences [see above], I entered my new password, and restored function.