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.
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