First, I'd suggest looking at Is is safe to plug a surge protector into a 2-prong outlet using a 3-to-2-prong adapter?. That may answer your question. I'd also suggest looking at the outlet box and seeing if it's already grounded, in which case you could just replace the outlet.
However, if it's protection against power fluctuations you want, I'd suggest a UPS, not a surge protector. They have an internal battery, and if you buy an Online/double-conversion UPS, the battery is always what's providing the power. They may well not like being without a ground.
First, neutral and ground are not the same thing. Neutral only handles normal current returns. Safety ground handles only fault currents. The two must never be connected to each other except at the service source. Abusing ground as a current return will "work" but defeats its purpose as a safety device. Actually it makes grounds unsafe.
You are fortunate that the long 1000' run seems to be intact. I have no idea what the story is with the yellow wire. Yellow is not legal for neutral (must be white or gray) and is not legal for safety ground either (must be green, yellow with green stripe, or bare... bare is not allowed for aluminum outdoors). Yellow is just another hot wire color. Is it a 3-phase pump? (Breaker will be a triple).
Wires must be the above-mentioned colors natively if they are 6 AWG or below. 4 AWG or larger can be black and then designated with appropriate color tape, shrinkwrap or paint. Wire that large would be reasonable given the very, very long distance.
Fortunately, wells are 240V and do not require neutral. Also fortuantely, ground can be retrofitted via a different route, so if one wire is borked, you can use the other two for hots and bury just a ground wire. You cannot retrofit a neutral wire and you can't abuse ground for neutral. Of course people on farms will anyway, but the animals Will Not Like It.
If it is in metal conduit, that is an acceptable ground path, but non-threaded conduit tends to rust out.
To use your searching tool, you need to disconnect the wires at both ends first. If the wires are left connected to the circuit, it will confuse the signal too much. Also it won't work in conduit, but conduit makes repair pretty easy, unless it's rusted out.
I would disconnect the wires on the supply side, and install a 22k ohm resistor across each of the pairs of wires, one at a time. Then at the other end, test whether the resistance between any two wires is 22k.
Best Answer
It's likely that at some point during the cut, one of the phases was shorted to the neutral; when that happens, the line to neutral voltage in the house will be 240V rather than the usual 120V, which is enough to do some damage.
It is not likely that shorting neutral to ground would cause any trouble at all. The neutral is bonded to ground both at your service and at the pole - that's normal.