Turning off one PC causes problems on entire network

First steps in connectivity troubleshooting:

1. ping the default gateway - failure indicates a basic L1 or L2 problem (cable, switch / Wi-Fi)
2. ping the DNS server - failure indicates a server problem (or routing for remote server)
3. run tracert 1.1.1.1

and add the results to your question as text, using the { } function.

You find both default gateway and DNS server in the ipconfig /all output.

Your problem description does look pretty weird though. Does the problem occur if you unplug the power and replug it without turning on the PC? If not, it's possibly a bad driver (leaving the NIC in a jabbering state on shutdown) - try updating it from the vendor's support page. If it does, you might want to replace the NIC.