An RC-682M is an Onkyo, but it is the part number for a remote control ... I think you need to double check your model #. But I would try powerline network adapters if you can't run ethernet cable to your desired location.
Your right it is a remote number. The AV/ receiver is a TX-SR605.
I need to be clear. Looking for a way to either connect blue tooth or wifi to receiver. Send signal into receiver so it will play on different rooms. All rooms are connected to receiver. It originally controlled with Logitech harmony remote It has neither WiFi or Bluetooth connection.