When you use a public IP address (like 126.96.36.199), there is no need for DNS resolution, but you are not flexible in changing the address afterwards. If you use a URI (URL) to the fully qualified domain name, you need to ensure that the name is resolved in all the environments you are running the App (Mendix Free Cloud, MEndix Cloud, AWS,….On-prem, Local computer)
When running locally, check in the Windows Command prompt:
tracert hostname like in the picture below:
It will prove that the URI (here www.google.com) can be resolved and that the networks can reach it.
Second, you need to test if the ports are open. For this you can use the browser/telnet/netcat (NC).
You mention that the host is reachable. This is true if you get a response if you use the URI in the browser:
When you publish the app in the cloud, all these conditions should be fulfilled. In the free Mendix Cloud, you should first test the hard-coded IP. If that works, but the URI does not, you should have a look at the DNS settings. If both fail, your Firewall in between the free Mendix Cloud and your Teamcenter Activeworkspace is blocking the incoming IP (range) or it needs some form of additional authentication (check with the Firewall team).
Go make it