Accessing Django Runserver on Shared Hosting
I'm betting that port 8000 is blocked. That explains the timeouts you mention in the last couple sentences: the firewall is set to simply drop the packets and not return any connection refusal responses.
You're going to have to ask your hosting company if there's a way around this, but there might not be one. At the least, they'll have to open a non-root port (8000 or something else over 1023), but the OS can't tell when it's you opening the port or something else, so it'll be a potential security hole (e.g. an intruder can set up something to listen for commands on that port, just like you are).
runserver wasn't really designed to be run on the production box. It's designed to be run on your development machine, with a small test database or something. This lets you get most of the bugs out. Then you push your code to a beta server, configured with the real server apps (e.g. apache on port 80) and databases and such, to do the heavy testing (make sure there's a filter for what IPs can connect, at least). Then you push to production from there. Or not; there are lots of ways to do this.
I'm developing a Django application on a shared hosting service (hostmonster) and am, of course, unable to access the runserver on the default localhost ip of 127.0.0.1:8000 over Firefox. The Django Project site's documentation details how to set up remote access to the run-server, but I'm not having any success with that. Setting the runserver to 0.0.0.0:8000 leaves it inaccessible. Though I figured it wouldn't work, I tried to configure the runserver to my home ip address. That gave me a "That IP address can't be assigned-to" error, as I'd expected.
So, I tried configuring it to my hosted IP, the one through which I SSH in the first place. That set up properly, but still was unable to access the address via Firefox. When I plug in the IP address on its own, I just get a hostmonster error page. When I affix the port number, the connection times out. When I plug in the IP, port number and the /admin to access the Django admin page I've created, I also time out.