Best way to connect to Modem

I have Century Link internet in my home. A ethernet cable runs from a box on the side of the house into living room wall plug. Only the blue pair of wires are in use. The wall plug the installer used though is a phone outlet plug. And a phone cable goes to my older netgear wireless router. Can I convert the plug to a regular ethernet plug for use with a newer router. Or can I use a RJ 11 to RJ45 adapter. And what are the chances the blue pair will be in the correct location?