Why doesn't my new @me.com email address work?
You may just need to wait.

I transferred my MobileMe account to iCloud on iOS 5 launch day. I encountered the same issues that you seem to be having in that when I tried to use the mail app on iCloud.com it gave me same error message as you received. When I tried to turn mail and notes on in the iCloud system preferences, it just hanged on 'starting'. All other features were working correctly.

I just trumpet it up to high demand on Apple's servers and decided to wait. I just tried now and my email is working from both iCloud.com and mail.app.