The nonlinear I-V characteristics of thin high-sheet-resistance Hg-Xe alloy films are examined within the context of the Kosterlitz-Thouless theory of the superconducting transition. In the regime below the vortex-unbinding temperature Tc, where logarithmically bound vortices can be broken apart by a transport current, we find that VIa(T). Comparison with theory allows us to infer the value of Tc and the mean-field temperature Tc0 from a(T), and the dependence of these temperatures on RN appears in approximate agreement with the microscopic theory of dirty superconductors. A systematic deviation appears to be consistent with renormalization of the vortex interaction close to Tc due to the presence of small polarizable vortex pairs, and can be described by an effective vortex dielectric constant c=1.2. Further evidence for this renormalization, which is a key feature of the Kosterlitz-Thouless transition, is obtained by examining the curvature of the logV vs logI plot very close to Tc. The current dependence of a(I,T)=d(logV)d(logI) is a direct measure of the spatial dependence of the vortex interaction, allowing a direct comparison with the analytic predictions of the renormalization equations. Satisfactory agreement is obtained using physically reasonable parameters.