One more thing you can try. See if under the WiFi settings section, under Advanced, there is a way to still set a Static IP. If not there, then do a Forget Network on your existing WiFi. Depending on the way the S7 is setup, you can either select the network and tell it to use a static IP under the "Show Advanced options" menu, or you have to manually enter a network name at which point you can enter a static IP under the "Show Advanced options".
That should get you connected and hopefully your network is the only one causing this issue. I didn't see whether you tried other networks to see if it worked. Going back to read again to see.
Okay, here is a thorough update. I still have the same issue with the IP Addresses not matching up. I have done the ##7 thing with customer service, taken the phone into the techs, which said it works perfectly, completed a network reset...multiple to be exact, and now have even tried bypassing the system and using the WPA button. All steps I've tried have failed. What's weird is I had the same issue with my S6 and after moving service to the S7, it's like the problem came within the service because the S6 can connect to the wifi fine. Even my wife's S7 connects with no issues. I reset the router and it didn't change anything. Also, as you guys pointed out, I checked the minimum # of devices that can be on the wifi and it's set at 50. Even with 4 people in the house, that's impossible. I'm not sure what to do at this stage outside of the obvious... settle for no internet on my phone at the house. I also checked with outside networks and it connects on other networks fine. I clearly have no clue what the issues are.