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A wild guess. And a good one! I pulled the router connection and left it off for 15-20 minutes. The only change on the screen was a red X on the network connection - to be expected. Apparently the PC port is unhappy seeing a 1:1 cable connected to a peer. Yes, I know about crossover cables...

I'll attempt to amplify and rephrase. With the network cable in place between the PC and the router everything is fine. The router is a combination landline phone, internet, and wifi type. If I remove the cable from the router and connect it to the extender's Ethernet port, the PC screen goes...

Discovered this while trying to set up a wifi extender. PC has only one enet port. Couldn't get extender to pair with router via wifi so I connected to the extender direct to the PC with an enet cable. When the cable is disconnected from the router and connected to the extender the screen goes...