Singlet-triplet spin blockade in a few-electron lateral double quantum dot is investigated using simultaneous transport and charge-sensing measurements. Transport from the (1,1) to the (0,2) electron occupancy states is strongly suppressed relative to the opposite bias [(0,2)-(1,1)]. At large bias, spin blockade ceases as the (0,2) triplet state enters the transport window, giving a direct measure of exchange splitting of the (0,2) state as a function of magnetic field. A simple model for current and steady-state charge distribution in spin-blockade conditions is developed and found to be in excellent agreement with experiment. Three other transitions [(1,1)-(2,0), (1,3)-(2,2), and (1,3)-(0,4)] exhibit spin blockade while other nearby transitions and opposite bias configurations do not, consistent with simple even-odd shell filling.