Thank you for replying. I think we might be getting closer to the source of the problem. I tried making a telnet connection to my server at port 25, but to no avail. A telnet connection to port 143 is working fine though.
I actually ran system-config-securitylevel-tui, and it showed that the firewall was disabled. (When installing CentOS, there are no options for enabling/disabling the firewall). I also tried the command iptables -F, and nothing happened.
I am starting to think that the SMTP server might be listening on a different port. How could I go about confirming this?