The TOR (The Onion Router) is a major clue! It is designed to connect to and route all its traffic through the TOR network which is established automatically when TOR launches. It effectively bypasses your local router's functionality when accessing the web. I REPEAT: It effectively bypasses your local router's functionality..
The improbable solution, your router, has become the prime suspect. Then there is th: update or replace decision. All things considered replacement is probably your best solution.
If we knew what it was we were doing, it wouldn't be called research, would it?
