Database Site Vs Comany Site

I'm on a short assignment to inventory and manage the fixed assets of a small company, and we've just bought a web-based database for this purpose. While I'm pretty good at administering/running local databases, the web part has me stymied. Our company is between IT people, and there's no one on site with any more idea than I have about what's going on!!

Here's what I have so far:

--The company has a website which I'll call "ourwebsite.org" -- which I think, from searching the IP address the website points to, is hosted by HostMySite.com.

--There's also a record in DNS Management with the same name (ourwebsite.org), but pointing to our little server's local IP address.

--I need to find a way to get my database -- which I can access on the network at (server's IP address)/database (ie 0.0.00.0/database) -- online. I tried creating records in DNS Management (for ex., assets.ourwebsite.org) that point to our server's IP (the one that, if I type it in on the network, I can get to the site I'm looking for), but get generic "can't find the page" or "can't connect to the server" errors, even after 72 hours, when trying to access it from off the network.

--If I browse to assets.ourwebsite.org/database on the server itself, I get to the website! But if I go to that page from any other computer, on or off the network, it doesn't work.

--The Server is running Windows Server 2003

So, what are my options? Do I have to talk to the HostMySite.com people to add this page? Shouldn't I just be able to use my server's name (ourcompanyadc.ourcompany.org) and have that route to the server? What's going on here! Is there a simple way to get a tiny local-server-hosted website online outside of the network?