Pretty much the only thing you can do is do domain "forwarding", where someone types "yourdomain.com" and it then forwards them to another domain name, such as icemanjc.kicks-ass.net (which is a dynamic DNS account that you set up at a place like dyndns.org). You can set up "masking" as well, so that the visitor always sees "yourdomain.com" in their browser's URL field, instead of "icemanjc.kicks-ass.net".
Without a static IP address (which you do not have, I'm assuming, because you're using DSL and only the upper-tier DSL plans offer static IP addresses), you cannot do "true" domain hosting, because of the entire internet DNS system that resolves names like "apple.com" to their IP addresses.
Look up "domain forwarding" on GoDaddy and go grab yourself a dynamic DNS account somewhere, and you should be good-to-go to host a single website from your server.
I have one set up similarly right now --
http://www.blowthesalon.com is simply forwarded to judas1012.kicks-ass.net, which is my dynamic DNS account with dyndns.org. I lose the benefit of being able to host more than one website (without some messy folder structure), but it works a charm.