  We study conductance fluctuations in a two-dimensional electron gas as a
function of chemical potential (or gate voltage) from the strongly insulating
to the metallic regime. Power spectra of the fluctuations decay with two
distinct exponents (1/v_l and 1/v_h). For conductivity $\sigma\sim 0.1
e^{2}/h$, we find a third exponent (1/v_i) in the shortest samples, and
non-monotonic dependence of v_i and v_l on \sigma. We study the dependence of
v_i, v_l, v_h, and the variances of corresponding fluctuations on \sigma,
sample size, and temperature. The anomalies near $\sigma\simeq 0.1 e^{2}/h$
indicate that the dielectric response and screening length are critically
behaved, i.e. that Coulomb correlations dominate the physics.
