I've got two machines, one AGS box and one web server. AGS 10.3 has been installed and has services running ready for consumption. On the AGS machine I can hit http://localhost:6080/arcgis/rest/services and see everything.
On the Web machine I get the following error when configuring the Web Adaptor. I tried using the URLs:
After this I tested hitting the REST endpoint from the Web machine. Hitting the URL http://agsserver:6080/arcgis/rest/services I get this:
I've used PortQuiz on both servers and can get out over port 6080 so I don't think this is a firewall issue. Both servers are running 2008 R2 and are in the same domain. SSL is not being used in this case since these are publicly available servers (as per the client).