As Bill said, 993 is usually IMAPS. Are you sure it's running without SSL? What happens when you do:
telnet serverip 993
Do you get a greeting? If not, what about:
openssl s_client -connect serverip:993
If you get a response in either, just type:
If you get a response from the first, what does it say? If you get a response on the second, it means you are running IMAPS, which means you need to change your config/config.php settings for your imap connection (see $use_imap_tls).
As a side, Courier defaults to limiting connections from a single IP to 4 connections. If multiple people will be using this SquirrelMail install, you'll want to increase that limit, see the MAXPERIP setting in the imapd config file.