It's probably not the internet as such, it's probably either some dodgy cabling or one of the machines on your lan is sending stuff that is confusing the tivo. (The kernel is rather ancient.)
So I would try a different cable and port.
I would also use wireshark to sniff on the network. Basically anything that show up while you are not doing any network traffic is a likely candidate.
It will be Broadcast or multicast, udp or icmp.
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