cooling problem!

Could it be that the heater core is plugged? If there is no flow though the heater core, it would blow cool air and it would cause the car to overheat at the same time.
 
it looks like the radiator itself is leaking. i recently installed a mishimoto. looks like its leaking terribly. its leaking from the upper hose area. i can see a wet trail going all the way down the radiator. anyone know what this could be?
 
a good way to put water in the car is to pull the t-stat and add water/coolant first and then put t-stat housing back on then fill coolant resiour. start the car. let the fan come on aleast two or three times with out having the a/c on or heater once you have done all that go and drive the car.