If I understand you right, you have a HTTP server set up on a box at home; for the sake of example, let's call it yourbox.somedomain.com. And you also have a GoDaddy account that contains a HTTP server.
In order to get users to be redirected to yourbox.somedomain.com, you need to do two things:
1. Make sure that the DNS system resolves yourbox.somedomain.com to the IP address of your box at home. It may not happen immediately when you make some change to some DNS server, because it takes some time before all DNS servers in the world notice the change you make. But once the DNS system comes up with the right IP address for your box at home, then you are in a good position to re-direct requests that currently go to your GoDaddy account.
2. According to the GoDaddy FAQ, if your domain is parked there (for HTTP purposes), then you can log in and tell it to redirect any queries to http://yourbox.somedomain.com
. I guess that if your domain is not parked there, but is actually being served as an active site from their servers, this will not work. Perhaps you can get them to park your domain there, so that you can then redirect it to your box at home.