We carry out Monte Carlo (MC) simulation as well as solution of the Chandler-Silbey-Ladanyi (CSL) equations with self-consistent closures for symmetric hard dumbbells with bond lengths L = 0.1, 0.4, 0.6, 0.8, and 1.0. The consistency conditions include the zero-separation theorems, the pressure consistency (P-v = P-c), and the overlap conditions. Conventional closures, such as the Percus-Yevick closure, give the wrong sign (negative values) for the unbonded bridge function B-00(r) for small bond lengths L < 0.8; the MC-determined behavior of B-00(r) being >0. This explains the failure of the common liquid state closures for chain molecules. The CSL is solved with a set of new closures. The new closure forms are flexible, and are required to satisfy the consistencies imposed. The results are at the same time consistent and highly accurate.