Yeah I have router And my computer is placed in DMZ. It is Linksys E3200. But even when I connect without it, there is no change. Also there should be another router that ISP uses to distribute internet to people in my house ... can't change or overcome that one.
And yes, I have real public IP behind that router. I used to host lots of games, and had TS server and FTP server in the past ... never got problem with connection from anywhere.
With ISP I have optic cable that is bridged from house next to me via some kind of wireless ... don't know what tech is used exactly.
So when you connected directly without router, you still can connect to server, but have endlessly rotating ship?
What your specs for your connection? What's your upload speed?