Here is information on the radio:
http://www.nostalgiaair.org/PagesByModel/969/M0005969.pdf
Electrolytic filter caps dry out over time and allow hum. They need to be replaced, item #36 in the schematic. Other caps will most likely be leaky and need replacement but replacing filter caps should remove hum.
Norm
My grandfather asked me to take a look at this unit. When you power it it makes a hum that get's louder and louder the longer it is on to a certain point. I am knew to these old units. Can anyone tell me what they think?