Solved Losing network connection

[cma6]

I have a wired Ethernet LAN with 5 PCs connected to router, which is connected to modem. Periodically I have to clear the modem because of a temporary internet service outage. For two of the systems, which share 1 ethernet connection through a switch, when I unplug modem and then plug back in, for those two systems only, the network (and internet connection) is lost and does not come back. On the two systems affected, the Ethernet network still has a name but shows "no connection." Any ideas?

 

[samuria]

From a cmd prompt type

ipconfig /all

post results

 

[cma6]

Retrieving network connection

In addition to the IP address, the following show enabled: DHCP, auto config, netbios over tcpip.

This morning I may have stumbled on the fix. In the past, when the cable co. sent bad data to modem, I could reboot modem and then after 5 minutes, all 5 systems would be back online. For no accountable reason, starting a month ago, when I rebooted modem, 2 of the systems lose network connection (semi-) permanently.
I tried quite a few fixes. I believe rebooting the router this morning fixed the issue. Also, later today when I had to reboot the modem, I first disconnected cable between modem and router and then rebooted modem: all 5 systems came back online in 5 minutes as in the past. So a reboot of modem is causing network issues for 2 of the systems on the LAN? What would cause that?