I disagree with ambience's direction. It is quite possible to have a web site respond only to IP, or only to names, or both selectively. This is likely one of two issues:
1) Your web site's host headers are not configured properly. In the default IIS configuration, IIRC, the "Default Web Site" owns the default host header, meaning all IPs with no name selection. That means any request that does not specifically match another site's host headers will be sent to the default. Did you disable this default site, or otherwise change its configuration? In the site you created, right click it in IIS, select "Properties", and click the "Advanced" button on the "Web Site" tab. That dialog is your host header set up for the site.
2) If your host headers are configured properly, it could be the server is not open to the internet. Have you checked your Windows Firewall configuration? Is GoDaddy providing any firewall or filtering functionality for your server?
