Windows reports “A network cable is unplugged” when the Ethernet adapter detects no cable link at all. The message is literal: as far as the PC can tell, nothing is plugged in, so the cause is the cable, the port, or the adapter itself.
The fix, in order
Reseat the cable at both ends. Unplug it from the PC and the router and plug it back in firmly until it clicks. Check that the cable is in the router's LAN port, not the WAN or internet port.
Try a different cable. Cables fail inside without any visible damage, and a known good cable is the fastest test.
Try a different port on the router. A single dead port is common, so move the cable to another LAN port and watch for the lights.
Check the port lights. A working link shows a light on the PC's Ethernet port and on the router. No light on either end means no link, so the fault is the cable, the port, or the adapter.
Enable the adapter. Press Windows key plus R, type ncpa.cpl, and check the Ethernet adapter is enabled. If it is disabled, right-click it and choose Enable.
Update or reinstall the Ethernet driver. In Device Manager, update the driver for the Ethernet adapter, or uninstall it and restart so Windows reinstalls it.
Do not force a cable into a port. An Ethernet plug only fits one way, and forcing it can bend the pins in the port and damage it permanently.
If it still happens
If no cable works in any port and the lights stay dark, test the same cable and router port with another device. If the other device links up, the PC's Ethernet adapter has likely failed, and a USB Ethernet adapter is a cheap replacement.
Common questions
Why does it say the cable is unplugged when it is plugged in? The adapter cannot detect an electrical link, which happens with a damaged cable, a dead router port, a loose plug, or a failed adapter. The message describes what the adapter senses, not what you can see.
Can a long Ethernet cable cause this message? A very long or poor quality cable can fail to link, especially past 100 metres. Shorter, better quality cables link more reliably.