Hi Jon, and welcome to the forums!
You probably started the IMAP proxy, and not the IMAP service. They're two seperate things.
If you don't know what the IMAP Proxy does, here's a good link:
http://wiki.zimbra.com/index.php?title=Perdition
To solve this, stop perdition, and start tomcat. Then login to the Zimbra Admin Console, and disable IMAP proxy:
Code:
su - zimbra
zmperditionctl stop
tomcat start
Good luck!
john