No - ethernet is not for cable only. It's more commonly used in commercial ADSL intallations, with multi-port routers - but also perfectly Ok for home use too. I have a number of friends who use ethernet - ADSL modems/routers.
You will need a different modem or router, however, one with a LAN/Ethernet input.
And I can't see any logical reason why this would solve your problem unless you are in a fringe area, and you get new, more sensitive modem/router.