If the motor runs and is turning the impeller it's unlikely that there is anything wrong with the pump.
Normally the first thing I check is if the pump discharge is plugged. Putting a short piece of hose on the pump and aiming it back into the tank is a quick check as to whether the pump is working. Then check the coolant line, I would blow it out with an air hose to check it.
Then make sure there is enough coolant in the tank to cover the impeller when the pump starts Open the coolant valve all the way before starting the pump, this will keep it from air locking.