Internet Cables – How to Safely Pull Internet Cable Out of Soil

No, the intelligent (budget-concious) solution in this case is to use the cat3 conductors and any of various schemes to run ethernet over them; starting with the base case that 10Mbit ethernet runs happily on Cat3 wire, and many Cat3 wires are actually fine for 100 Mbit. Those are "free" solutions.

You could put trunking switches on either end and run a bunch of 10 (or 100 if you get lucky) mBit connections in parallel (there will be a lot of pairs - likely 25, so you can run up to 12 wait, you say 50 or 100, so 25-50 - only takes two pair each) for pretty cheap. Except you went and yanked on and broke the wires already.

You can get two-wire "ethernet extenders" that will happily run 40 mBit or more on a single pair. They cost a bit more, usually. Your wire abuse also lowers the odds on those, unfortunately.

Thus, the correct solution for you in this case is to ignore the wire you have been abusing and put a couple of 5 GHz Point-to-Point radios on the buildings where they have a clear line of sight between them.

Or dig a trench and install fiber optic in conduit. That certainly is the "price no object professional approach" and has the benefit of being unaffected by thunderstorms which can wreak havoc with copper inter-building connections. Digging up the old cable is not normally a part of this approach, since it just adds a headache. Calling DigSafe several days before starting is a part of it, though...

When you pull on the wires, you are probably pulling against the telco's strain relief when you snap them. Virtually all "old phone cables" were installed by Ma Bell and she didn't just dump a cable into the ground. Which is to say, yanking the wires out is not going to work.

Simply call your cable provider to come hook you up to internet. If need be, they will replace the cable, otherwise they will simply terminate it.

Your "companioned electrician" is misinformed, as are you. You don't need triax or biax for getting internet from the cable TV folks, even though there are other systems which use such cables, mostly hoary antiquities at this point in time. A coaxial cable has two conductors - they are, not surprisingly, coaxial - a center conductor, and a shield, which is also a conductor. Which makes two conductors, not one.

Regardless, just call your cable internet, TV, etc. provider and ask them to hook you up. The vast majority of CableTV internet comes in on exactly the same cable as the TV does, though if the cable is in poor condition due to age or abuse they may choose to replace it anyway. They have specialized test devices the installer will use to check the signal levels at the cable and determine if it will work. Since those are specific to the cable system and typically have a pricetag near that of a car, it's not a DIY project, it's a part of their service provision.