EDIT: If the internal IP of the server works but the name of the server doesn't work, try adding an entry to your hosts file on the server when the web adaptor is installed. Location - C:\Windows\System32\drivers\etc
Add the internal ip and the name of the server.
We had been experiencing the exact same issue except we aren't using Amazon. During configuration we could use the internal IP, but the link for the services at the bottom of the screen returned the error: The remote name could not be resolved [server name].
Hope this helps.