How to calculate total impedance of two parallel conductors
Inductance:



The above is the formula for the inductance of parallel wires where s is distance between wires, L is the overall length and d is wire diameter and here is a calculator that uses the formula.

Capacitance between two parallel wires is:







For series resistance you will find many references on google for this and please note that it is ambient temperature dependant. There are plenty of references for skin effect also but not so many for the formula for proximity effect but hopefully this reference from wiki might prove useful.



Finally, once you have the resistance, inductance and capacitance you can use the standard formula for characteristic impedance (applies to any length of wire of course and is still valid down to DC): -



You haven't considered "G" but this is usually a very large resistance and its effect is negligible.

So now you have the impedance looking into an infitely long line of cable. However, you want the impedance looking into 100 metres of such cable so you will then have to work with reflection coefficients and the load impedance (stated as unloaded in the question) BUT YOU CANNOT ignore these load effects (and reflections) if you want a proper answer.

Reflections will occur with any incorrectly terminated cable: -



And these can effect results significantly even at moderate frequencies like 100 kHz. At 100 kHz the wavelength is 3 km but this is probably going to be more like 2 km. Major things happen at a quarter of this wavelength i.e. an open circuit can look like a short circuit and a short circuit can look like an open circuit so 500 metres is still pretty close for creating major errors when considering a cable that is 100 metres long.