You didn't tell how you know it is sending data. Many look at blink lights on a router and think that's it. However it is not unusual for a router to respond to PING and such will look as if there is data flow.
I install satellite internet for a living. I'm not new to computers.
Today I ran across something disturbing. A customers computer that was still sending information via the LAN connection onto the internet after power shut down!
Let me say the computer was not asleep...I checked. It wasn't powering off, it was dead as a door nail shut the *&%$ off!
I know of nothing that can perform this miracle of technology short of government intervention. Please someone tell me you know of a virus that can do this. Otherwise I believe I may have just left an FBI stakeout!
I don't have any specifics on the computer. I just want to know for curiosities sake if anyone has ran across this before.