The only function performed by the Ethernet on a TiVo is for multiroom streaming between TiVo/V6, and in-home streaming/downloading via TV Control. If you're doing neither, it's doing nothing.
Check your heartbeat light on the front-left of your TiVo - this is the status for the in-built modem. Is it flashing or static? If flashing - that's the on-board modem failed and a trigger for the box to be replaced with the newer V6. Same stable software but much newer and better hardware.
And that does use the Ethernet cable for the 'net connection....