A couple of things then:-
- what happens when you login from a client machine?
You could be hitting an issue where the server will reject the request as its coming from itself.
See this article on approaches to fix, I recommend the BackConnectHostNames approach.
You will need to reboot the server after implementing the registry fix.
Make sure you add all the Web Application URLs that you can access SharePoint using, think about the mysites web application and central admin.
To ensure SharePoint and IIS respond to the url https://intra.sharepoint.com you will need to do the following:-
- ensure that you can resolve the name intra.sharepoint.com to the IP address of your server that is hosting SharePoint. Create a host entry in c:\windows\system32\drivers\etc\hosts file. If your server has the ip address 192.168.1.10 then add the entry 192.168.1.10 intra.sharepoint.com
Presuming that we only have https://intra.sharepoint.com bound to port 443 and we have a single IP address assigned to the server then you could remove any SNI bindings for the SSL connection in IIS.
Lastly setup SharePoint Alternate Access Mappings through Central Admin->System Settings->Alternate Access Mappings and add https://intra.sharepoint.com as a public url.