Thank you for a detailed reply. I have gone through the things you asked me to check. There was an entry in netstat -an like this:
TCP [::]:8080 [::]:0 LISTENING
Which suggests that Apache is running. So now what I did was, I tried to add a Listen directive to the IPAddress the subdomain was resolving to.
Listen 123.45.6.789:8080
I also added a virual host entry explicitly for this IP
<VirtualHost 123.45.6.789:8080>
ServerName subdomain.example.com
</VirtualHost>
When I restarted Apache it failed with the following error:
"Context of the address was (OS 10049) request is invalid. : AH00072: make_sock: could not bind to address 123.45.6.789:8080"