  We investigate the zero-temperature transport of electrons in a model of
quantum dot arrays with a disordered background potential. One effect of the
disorder is that conduction through the array is possible only for voltages
across the array that exceed a critical voltage $V_T$. We investigate the
behavior of arrays in three voltage regimes: below, at and above the critical
voltage. For voltages less than $V_T$, we find that the features of the
invasion of charge onto the array depend on whether the dots have uniform or
varying capacitances. We compute the first conduction path at voltages just
above $V_T$ using a transfer-matrix style algorithm. It can be used to
elucidate the important energy and length scales. We find that the geometrical
structure of the first conducting path is essentially unaffected by the
addition of capacitive or tunneling resistance disorder. We also investigate
the effects of this added disorder to transport further above the threshold. We
use finite size scaling analysis to explore the nonlinear current-voltage
relationship near $V_T$. The scaling of the current $I$ near $V_T$,
$I\sim(V-V_T)^{\beta}$, gives similar values for the effective exponent $\beta$
for all varieties of tunneling and capacitive disorder, when the current is
computed for voltages within a few percent of threshold. We do note that the
value of $\beta$ near the transition is not converged at this distance from
threshold and difficulties in obtaining its value in the $V\searrow V_T$ limit.
