Why is https not working?

OK, try this:

telnet localhost 443

Does that give a response, or does it hang? If it's responding, you should get something that looks like:

$ telnet localhost 443
Trying 127.0.0.1...
Connected to localhost.localdomain (127.0.0.1).
Escape character is '^]'.

(if telnet is not installed, then install it; you can exit the telnet session by hitting control-] and then typing "q" to quit)

If you're able to connect to the web server on the local interface (and the web server is running, given your logs), then there is a firewall issue (I know you said you haven't set the firewall, but this will confirm). In that case, run:

iptables -L -n

and post the results.

Update

From comments, this is an EC2 instance, so look at the Security Groups associated with this instance. Make sure you're allowing tcp/443 in your Security Groups.

Something like this might help:

http://cloud-computing.learningtree.com/2010/09/24/understanding-amazon-ec2-security-groups-and-firewalls/

On dual-stack hosts, listening to ::443 means you're listening both on IPv4 and IPv6. Test the TLS negotiation yourself:

openssl s_client -connect localhost:443
[lots of negotiation output, to ensure the basics are there]

Then you'll be able to test if HTTP replies:

GET / HTTP/1.0

Here's how I'd redirect:

<VirtualHost *:80>
    ServerName mail.example.com

    RewriteEngine On
    RewriteLog /var/log/apache2/rewrite.log
    RewriteLogLevel 4
    RewriteRule ^(.*)$ https://secure.example.com/mail$1 [R,L]
</VirtualHost>

Please remove RewriteLog and RewriteLogLevel in production, or risk getting a disk filled senselessly.