Ok. Found some DNS settings on my router, and fixed the internal domain name "problem" but it's still only internal. If I set my public IP(internally) it doesn't connect.
I can connect to an internal computer from external, even though the client says "not ready".
I cannot connect from internal to external computer. Instantly shows "remote desktop is offline"
This leads me to think that somehow I have something wrong in router settings, or I have a security feature blocking something. I just don't know enough about routing to know where to look.