Problem with parallel flow
Sometimes centrifugal pumps (those with a spinning impeller) will cavitate when there is a discharge path too big to supply back pressure, and/or if there is not enough suction pressure. Cavitation will result in low or no flow, and will usually be accompanied by pump noise. You may be operating the pump outside of it's design parameters (pump curve). 

See if you can recreate the "no water" scenario, then slowly close off the pump discharge partially to provide some back pressure (which is what it sounds like you did when you blocked/removed the flow path to the 3/4" pipe). If the pump is cavitating do not run it for too long like that or it could be damaged.