OK, I was only partially right. And I continue to follow up with my problem so other whom may stumble upon this can figure it out.
Yes,if you turn off wake up shutdown the computer will shut down and stay off. However, it also disables the wake on LAN. The real secret (as to which I don't fully understand) the problem was in the type of item accepted to turn on the system. In the same area as the shutdown wake up (device manager, LAN card properties, advanced tab), one of the items has a list of what can turn on the computer. I set it to all. I am guessing that bc it accepts everything, it may have misinterpreted network noise from the router. As I said though, this is a guess. So, I changed the type accepted to ONLY magic packet and viola, everything works as it should. Wol to start it and it stays shut down.