You should post a copy of the diagnostic text that you see when you use the standard Roon client (desktop or mobile) and go to Settings → Roon ARC.
This will give us much more information to go on.
If, in your router, setting your Roon Server to be the DMZ works (albeit with the serious security issues that that presents), then it is likely that your port forwarding setup (in your router) is incomplete or incorrect. It should be easy to fix.
As a matter of principle, if you have a single router setup, then uPnP, if supported by your router, should work. If it does not, a single manual port forwarding rule forwarding TCP connections on the ARC port (as shown on the Settings → Roon ARC page) to the ip address of your Roon Server should work.