Dovecot authentication error, port also not open?

I've been meticulously following this guide on setting up a basic email server using Postfix and Dovecot on Ubuntu. I'm using an Amazon AWS server, which is also running an apache server for a website.

I followed the guide to the letter, and both Postfix and Dovecot start up without any errors. However, when I try and get Thunderbird to connect, I get an error which I've seen in many of the other Server Fault questions I read before posting:

Aug 18 09:52:44 ip-172-31-59-35 dovecot: imap-login: Disconnected (no auth attempts in 0 secs): user=<>, rip=174.119.redacted, lip=172.31.59.35, TLS: SSL_read() fail3_READ_BYTES:tlsv1 alert unknown ca: SSL alert number 48, session=<Jgoli1U6LQCud4oF>
Aug 18 09:52:44 ip-172-31-59-35 dovecot: imap-login: Aborted login (no auth attempts in 0 secs): user=<>, rip=174.119.redacted, lip=172.31.59.35, TLS, session=

I am really scratching my head on this one. The other strange problem is that both an nmap port scan and netstat -tulpen show port 465 as closed. I would be happy to post my full main.cf, master.cf, etc. but it's essentially identical to the ones in part 2 of that guide. I've triple checked those files for simple typos or omissions, and everything seems to be there (as I said, everything starts up fine without errors).

As far as the DNS setup goes, the domain is registered using GoDaddy, and I am pretty confident that I have the DNS records set up correctly -- I mean, the mail server IS detecting a client trying to connect, it's just throwing up all over it instead of giving it mail access.

I would be happy to grant some access to the server, and/or post whatever files are needed here.

Thanks!

EDIT: As stated below, the IMAP functionality DOES actually work, despite throwing those errors when Thunderbird probes the server. However, the SMTP functionality does not work at all -- any attempt to log in or send email results in an error saying the server is either refusing connections or not running (which coincides with my discovery that the port is closed). I am still very confused as to why this is happening.

EDIT2: Using sendmail, I can easily send a test message as follows:

mail -s "test message" [email protected] < message.txt

Though gmail picks it up as spam (as it's being sent from an internal account), it does actually work... so the problem is between the client and the server, not the server and the relays.