Oh, I missed it, you tried system restore.
Well, I thought the computer worked, and now it doesn't work, but if the ports on your router/gateway are not open for the application, that could be a problem, but then the question is, how did the gateway work and then stop working?
How many restore points did you try? Maybe an even earlier one would do the trick.
Again, sorry for not catching that you tried system restore, although there are usually several restore points, so maybe you only tried one restore point? I use it to fix unexplained changes at times, but as you indicate, it's not a perfect solution and may not work at all.
Jeff