maybe some details of your router and the type of connection you have from your ISP would help, but to get started .....
Is there some specific reason you are aware of for you to be going through the means of connecting you outlined?
in the usual circumstances the connection details for your ISP are entered in the router and this holds the connection open.
A PC is then connected to the router via eth and is able to access the internet from this connection through the router.
Unless there are other reasons for doing differently, I suggest you set up the internet connection (PPoE) in the router. You should then be able to use eth connection from the PC permanently.
If you need more specific assistance in setting up the router please post back its make and model number.