Ethernet cannot see RTA1025W modem (wi-fi can)
Do you get the same result when starting up in safe boot?

This could either be an Ethernet driver or a hardware issue. One of the first things to try is perform an SMC reset (shift-ctrl-alt-power). I usually go a stage further and disconnect the battery for 10 minutes, this can clear SMC-related issues that the official method doesn't always cure such as errant SD card readers disappearing etc.).

After an SMC reset perform a PRAM reset (alt-option-p-r).

Your problem should be cleared by this stage but if not you need to look at your preference files in /Library/Preferences/SystemConfiguration, particularly NetworkInterfaces.plist and preferences.plist. Move them to your desktop, reboot and see if connectivity is restored.

Another way to check if it's a software issue is to create a clean install of OS X on an external drive. If your Ethernet port is working under the new OS then you will know it's definitely an OS problem rather than hardware.