We parameterize Hubbard and spin models for EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ from broken symmetry density functional calculations. This gives a scalene triangular model where the largest net exchange interaction is three times larger than the mean interchain coupling. The chain random phase approximation shows that the difference in the interchain couplings is equivalent to a bipartite interchain coupling, favoring long-range magnetic order. This competes with ring exchange, which favors quantum disorder. Ring exchange wins. We predict that the thermal conductivity, $\kappa$, along the chain direction is much larger than that along the crystallographic axes and that $\kappa/T\rightarrow0$ as $T\rightarrow0$ along the crystallographic axes, but that $\kappa/T\rightarrow\textrm{a constant}>0$ as $T\rightarrow0$ along the chain direction.
