how to calculate DC resistance of transmission line from telegrapher's equation
I figured out the answer to my question.  Yes, you can use the Telegrapher's equations to compute the DC resistance when a transmission line is terminated with a short and when G (shunt conductance) = 0.  The key to using the equations is to keep G as a term but assume it to is very small at the end so that you can use the asymptotic behavior of the functions that is in.  I'll explain below:

Using the boundary conditions for the short terminated wave equation, the constants A and B for the voltage TL equation can be determined.  These are A = Vs/(2*sinh(gamma*Lwg)) and B = -A. 

Input impedance is simply V(x,s) / I(x,s), 

where

I(x,s) =  A/Zc * exp(-gamma*x) - B/Zc * exp(gamma*x)

x = 0 at shorted end and x = -Lwg at source end.

Zc = sqrt((R + sL)/(G + sC)) (see Telegrapher's equations)

gamma = sqrt((R + sL)(G + sC))  (see Telegrapher's equations)

Plugging A and B into V and I and calculating V/I gives:

V(x,s)/I(x,s) = -tanh(gamma*x) * Zc

At DC, Zc = sqrt(R/G)

At DC, gamma = sqrt(RG)

With x = -Lwg, we get

V/I = tanh(sqrt(RG)*Lwg) * sqrt(R/G)

if G is very small, tanh(sqrt(RG)*Lwg) will be approximatley sqrt(RG)*Lwg

And thus V/I = sqrt(RG)*Lwg * sqrt(R/G) = R*Lwg  

This is the result I was expecting.