What we're all missing here is:

I have the Tivo hooked up to my machine, which is connected (wirelessly) to the Linksys router

Which means that you probably have no desire to run a cable from the tivo to the router, which is what everyone is sugesting because that' the normal "right" way to do things.

If we have cable/dsl modem -> router -> windows pc with ICS -> tivo, it should work(i think. multiple levels of NAT might complicate things to the point that ics gets confused). The windows PC will be assigning your tivo an address, and as far as I know you won't be able to "see" what that IP address is. You will know the IP address range, and can easily scan the suspected addresses with a few pings.

You might just want to buy a wireless bridge for it. Though that would be more expensive and the above should work.

Matthew