Then the problem is with your router/gateway/firewall. You need to configure it to connect to the machine. Be aware that some firewalls don't allow you to connect to the external IP address from inside your network. You may need to test it externally, using a smartphone with RDP installed, for instance.
I factory reset the router, and all works fine now. solved
I found this worked in my case. First of all, the IP vs no-ip made a difference, as noted previously. The only other thing that made a difference for me was that after getting the authentication pop-up dialog box - was that I could *not* use my "email address" Microsoft logon, but had to use my regular non-email address Local Account logon (which I suppose you would have to create first if not already setup - See https://support.microsoft.com/en-us/...-in-windows-10 ). Then, if prompted, allow the Certification access. That did the trick for me.
Something else to look at if all other advice has failed. Keyboard settings. We recently setup a new HyperV virtual PC and installed Windows 10 N. Despite everything we tried, VPN would not work for the admin user, not even on the internal network (so not a router issue). After hours of changing firewall settings and rules, etc, the dev decided to give it one more go and update the user, using a password without symbols and viola! His laptop uses US keyboard and the default for 10 N is a UK/European keyboard - while he was hitting the same key sequence, effectively he was not entering the same password... Hope this might save someone else hours of frustration when this page comes up on their search for 'rdp not working on windows 10'. It might seem obvious now, but when you use only one keyboard layout for the vast majority of your working life, it's not the first thing that springs to mind when installing a slightly different version of an OS you have installed so many times before without a hitch.
It's the Firewall within Win 10. Check the RDP settings there.
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