Need some clarification here.
You say you're connected by a Sky adapter. Is that the only way you've ever connected? That's a device for connecting a Sky box to WiFi, so a little odd. You say the PC is "also" connected to WiFi. So for clarity, does the PC have it's own WiFi adapter? Maybe right-click Start > Device Manager & report what devices you have listed under Network adapters.
If you are indeed using the Sky box as a WiFi adapter, then that connects by ethernet. A problem there might explain why you're getting an ethernet error. First thing to check is that the cable in the green socket of the Sky adapter is connected to the ethernet port of the PC & that the Sky adapter has power. If all is good try resetting the Sky adapter. Looks like the usual paper clip in the hole at the back, hold it in until something happens with the lights on the box. Then reboot the PC & see where you are.
If still no joy go to Settings > Network > Change Adapter Options & you should see a screen with all network adapters. Double-click the ethernet adapter & select Properties. Make sure that Internet Protocol V4 is ticked & then double-click it. Make sure both options are set to obtain address automatically. & OK back to Settings. Then reboot the PC.
Hopefully one of these steps will re-establish the ethernet connection to the Sky adapter & you should then see the new router.