I need to clear up a couple of things here... One cannot normally network with telephone wire. This especially true for the kind of flat, untwisted wire available in hardware stores, etc. However, one can network with twisted-wire other than CAT 5 UTP. There are other categories of wire that will allow networking at lower frequencies.
CAT 2 1 Mhz Telephone wire
CAT 3 16 Mhz Ethernet 10BaseT
CAT 4 20 Mhz Token Ring 10BaseT
CAT 5 100 Mhz 100BbaseT
I prefer to use CAT 5 (or CAT 5E) cable and connectors for all new installations.
In this particular case we do not know what category of cable has been used. We do know that a cable MODEM operates at a much lower frequency than an Ethernet. We do not know if the cable MODEM has a 10BaseT or 100BaseT Ethernet interface. We dont know how long a cable like the one used can be and still work reliably with a cable MODEM. I would guess, from my work many years ago with RS-432, balanced voltage connections, that it would be a significant distance. In mid 80s we connected a DEC PDP/1170 min-computer to the forerunner of the Internet in Germany balanced voltage amplifiers at 56K for about a 1/2 mile through a very noisy, relay-operated telephone system built in the 1930s.
All in all this experiment is interesting and might save some work and money when wiring a cable MODEM. It is easy enough to do and I would certainly try it before running CAT 5 cable between two floors of a house. If anyone else has luck trying to connect a cable MODEM this way, we would certainly like to hear about it. Larry