We find evidence of a hard X-ray excess above the thermal emission in two cool clusters (Abell 1750 and IC 1262) and a soft excess in two hot clusters (Abell 754 and Abell 2163). Our modeling shows that the excess components in Abell 1750, IC 1262, and Abell 2163 are best fit by a steep power law indicative of a significant non-thermal component. In the case of Abell 754, the excess emission is thermal, 1 ke V emission. We analyze the dynamical state of each cluster and find evidence of an ongoing or recent merger in all four clusters. In the case of Abell 2163, the detected, steep spectrum, non-thermal X-ray emission is shown to be associated with the weak merger shock seen in the temperature map. However, this shock is not able to produce the flatter spectrum radio halo which we attribute to post-shock turbulence. In Abell 1750 and IC 1262, the shocked gas appears to be spatially correlated with non-thermal emission suggesting cosmic-ray acceleration at the shock front.