The TiVo doesn't use the Ethernet port for an internet connection, it has an internal modem.
On the front-left of your TiVo are a series of green lights - the second-from-left has a painted "heart" symbol next to it and is your "online" light giving a status of the TiVo's inbuilt 'net connection.
Static on is good, flashing green is bad and means the internal modem is failing or has failed. That's a service fault.
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