When I turn on my STA-RITE 1.5 HP pump, it makes a humming sound.

A humming noise is fairly normal if the pump is running and pumping correctly. I am guessing this is not the case. Usually it is just a stuck impeller that is the culprit. Power down the unit and open the pump housing to access the impeller. Then gently turn the impeller feeling for resistance (some resistance is normal from the magnets of the motor). If everything seems ok close and secure the pump housing. Try powering the unit on and see if it starts up correctly. If it is still having issues manually prime the pump. If the pump runs correctly for a few minutes after manually priming but slows or stops you have a leaky seal or fitting to find. Finding the seal is not hard but will take a little time and patience. With your garden hose, very carefully run water over each joint and fitting with the pump running. It will take a minute or so of water running over a leaky seal for the pump to prime so take your time. Make sure not to get water on the motor as it can deliver a very nasty shock and destroy the motor. If none of this gets you up and running the cause may be the motor is bad and needs replacing.