It shows up on NameCheap as taken because you've already purchased it at GoDaddy. NameCheap & GoDaddy are what's called Domain Registrars. You can register a domain, any domain (with some limitations,) at any Domain Registrar.
When I go to your domain, I get a parked page. Per WhatsMyDNS, you have a conflict of IP addresses. So, your site not showing up is a DNS issue. Most likely it's propagation, which can take 24-48 hours. You may want to contact phone support.
I am a GoDaddy End User - Just Like You Check out my site! | I drink and I know things. Especially about websites and web hosting. * Please note that I offer free advice on this forum. If you would like personalized help, please contact me. Otherwise, please ask your question in the proper forum so the answer can assist EVERYONE in the community and not just you. Thanks! *
Once your issue is resolved, please be sure to come back and click accept for the solution