Ethernet Switch, Unable to identify more than one computer

I can not get more than one computer to connect. All but one get "Unidentified network" Public Network in the Windows network and sharing center window. 

I have the approved and reccomended Motorola MBB8600 modem, works perfect with one computer. I tried connecting, one at a time, each of the following switches. TP-Link TL-SG1016D 16 port gigabit switch and D-Link DSS-16+ switch. One computer, first one connected to switch will connect. Any other computers connected to it will attempt to identify and connect but end up with "Unidentified network" Public Network in the Windows network and sharing center window. I assure you it is not the computers, I am a pro with them. I did though try all kinds of things, even reinstalling the network drivers on one computer just to be able to say I did all of that. 

Both of these switched Do Work Fine on my existing ADSL network. I have a lot of windows computer software, network, and hardware experience. I have a lot of ADSL network experience.

Please suggest what I might consider next.