That's the way it looked on the previous Win7 server which worked for a few years for me that way. Pretty sure that's *probably* not the problem.
But I continue to really struggle with this. I ended up spinning up a new 32-bit Win7 VM, just turned off the damn Windows firewall on it. After getting everything installed, it was about a 50-50 chance of the server coming up with the checkbox in the Post Game to Internet. However, it still wasn't showing up outside my network, so to just take out all routing variables, I added that machine's IP (which is static IP I set) to the router's DMZ. Still a no-go.
Now, even when I restart the machine, even with the Firewall turned off on the Win7 machine, and even with that internal IP in the router's DMZ, that 'Post to internet' box is grayed out with no check in it. Again. W.T.F.
The host for this VM is on a work machine that has a plethora of group policies pushed down to it. I am the admin on the box, but it is possible that network/port group policies on the Hyper-V host could be affecting the Win7 VM?
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EDIT: So I think I figured out why I was getting a 50-50 chance of having the server come up with a checkbox in the Post Game to Internet field: if I pin NWServer to the taskbar, and then immediately click on it as soon as I login to Windows, it will come up with that checked. But if even a couple seconds pass, or I try to bring it up again, that check is always gone.