Oh, that? That's the secret information that Empeg is collecting from your computer. They had special circuitry put in which keeps the 10bT card powered up even when the player isn't. They plan on collecting all of the data and selling it to Microsoft to cover the cost of their WMA license.

Er... Seriously though, Ethernet doesn't work that way. No power = no Ethernet. Not sure why your router is blinking, mine doesn't (Linksys BEFSR41.)