Vintage Synth Repair

Do you have several pieces of equipment plugged into the same outlet?  This might be causing a ground loop that increases in strength after the equipment has been powered on for a short period of time.  Does the hum remain when no voices are being sounded?  More likely a ground loop.  Try plugging the other equipment into a different outlet across the room with an extention cord. 
 Is the hum only present when certain instrument voices are played and is not present when other voices are played?  More likely to be a voice programming issue.  The organ voice is most likely of all the voices to be a sine wave (or close).  A hum is usually a 120 Hz sine wave.  That is about the B or B flat in the octave below middle C.  Does playing that B flat note on organ voice sound either louder or softer than the other notes?  Does that B flat have a 'LFO-type' waving sound that the other organ tones don't have?  All signs of a ground loop.
  Do you have an oscilloscope?  Do you have a sound-card oscilloscope program?  Download a scope program and feed the hum from the synth into the PC audio line input.  Run the scope program and see if the hum actually is 120 Hz.  If not, it's a synth hardware issue. If it is, then it is a synth power supply problem or a ground loop.