Running Ethernet over two phone lines
Your existing voice grade phone wiring is probably no better than Cat3, if even that. So you'd probably struggle to get 10BASE-T to work, and 100 mbps and Gigabit Ethernet is probably out of the question.
10BASE-T (10mbps) was the last widely-available flavor of Ethernet that was designed to work over Cat3 voice grade wiring. So assuming your existing phone wiring is even Cat3 (note: untwisted telephone line cords are not), and if you have two pair, you could possibly use them for 10mbps Ethernet.
What's commonly called "100BASE-T" is actually "100BASE-TX", which requires two pair of Cat5. There were two competing IEEE standards for 100 mbps Ethernet over unshielded twisted pair (UTP) wiring, but they were never widely deployed: 100BASE-T4 (required 4 pairs of Cat3) and 100BASE-T2 (required 2 pairs of Cat3). I don't think you can find any 100BASE-T4 or 100BASE-T2 NICs or hubs/switches anymore, because you could barely find them when they were new in the 1990's.
Gigabit Ethernet (1000BASE-T) requires 4 pairs of Cat5.
The IEEE stopped caring about voice grade wiring after 100BASE-TX was a huge market success while 100BASE-T{2,4} flopped.
I suppose it's possible that given a short enough run of Cat3 that you could get lucky and happen to get 100BASE-TX or 1000BASE-T to work, but it seems unlikely to me. I think there's a decent chance you could make 10BASE-T work, but even that isn't guaranteed without knowing for sure that you have good Cat3 end-to-end, and you're wiring it like Ethernet (point to point) and not like home phone wiring (which often has branches or multiple jacks on a long passive bus).
I currently have 10baseT running on telephone wiring that predates the cat3 spec by 5 years (cable says it was made in 1987 by Essex -- obviously prior to their merger with Superior and forming what we know today as Superior-Essex) and that is at distances approaching or exceeding the 358 foot / 100 meter limit. None of these 10baseT runs are showing any errors in the switch.
Many of these runs have two cross-connects and four 66 blocks on them.
My suggestion---give it a try. It will likely work at 10baseT speeds but you must set the speed at either the switch or computer end; autonegotiation will try to make it work at 100baseT or even gigabit speeds, which is probably not going to work very well over existing telephone wire.
You can get 1 GB over short distances of Cat 3. I had my house wired with 8 conductor Cat 3 in 1994. I have been able to upgrade most of the house to 1 GB speed using all 4 pairs. The furthest terminations (100') only acheive 100 mb, while terminations under 90' seem to be able support a stabel 1 GB connection.