Wait a sec. Ethernet uses 1,2,3 and 6, so I don't need to re-wire if I only have 2 twisted pairs... right?

Well, it depends on how those wires are hooked up inside the walls. If they connect directly to each other (for instance, if all of the jacks in the walls are connected to the same wires), then you need to rewire.

If you have a completely separate run of 2-pair cable for each and every jack in the house and they all converge in a central location such as a wiring closet, then you can put RJ45 jacks at each end of each of these existing wire runs, and they will work as ethernet cables as long as you get the right pairs on the right pins at the ends of the wires, and you put a hub where all the wire runs converge.

But if all these jacks are wired to each other and the wires are all connected together (essentially making them into one long wire with multiple cut-in points at each wall socket), then they are wired for a telephone and cannot be used for ethernet.

I'm just confused about how this house is wired. From your description, it sounds like a standard four-wire telephone system with standard two-line analog telephone wiring. I can't imagine someone wiring it to be ethernet-capable with only two pairs.