@ nunyo:
You should open your Realtek PCIe GBE Family Controller Properties and under the Power Management tab, uncheck “Allow this device to wake the computer.”
If paranoid, you might also check your motherboard BIOS and disable any setting for “Wake On LAN” or WOL.
Judging from your post, you don’t need that wake function. Note, this will NOT affect any other remote or background services you might rely on or be subject to (malicious or otherwise) except in that they can’t run when your computer is “off.”
Cheers.