Well if you can see your 1 Hz square wave pulses through the cable, that's better than nothing. At least it shows the conductors don't seem to be broken.
And you are getting good voltage, which is also good.
And your arduino is capable of pulling the wire down close to zero volts, which would tend to suggest that your pull-up resistor isn't too small.
The point is, due to the capacitance and inductance of the cable, that square wave gets distorted and has sloping rises and falls and overshoots as the frequency increases. This happens with any kind of transmission through any kind of cable, and it limits both the frequency and the length of cables you can use.
For example, normal ethernet won't work for more than about 500 metres, or whatever it is. On the other hand, SPI might not work if the wires are longer than 20 centimetres.
But we know that many people have succeeded at getting DS18B20's to work at distance over 10 metres, and up to at least 30 metres. So you should be able to, also. I don't know why you can't. I am pretty close to out of ideas.....