make sure disabling your firewall, and trying to connect using telnet, us should using username and password users on telnet, this is for testing only.
ex:
$ telnet mail.mycompany.com 110
Trying 200.0.0.1...
Connected to mail.mycompany.com (200.0.0.1).
Escape character is '^]'.
+OK International Company, LTD. Zimbra POP3 server ready
user
myname@mycompany.com
+OK hello
myname@mycompany.com, please enter your password
pass [mypasswordhere]
+OK server ready