Soft hum at no volume in tube clock radio

[DavGoodlin]

If the hum is varied with volume pot, try grounding the center terminal in the volume control (likely connected to grid of 1st audio tube).
Then try grounding the low side of the volume pot.
If hum stops, you either have a bad ground connection to the pot low side or a bad pot.

Try jumping a 47 mf [>16 volts] capacitor from the 35C5 cathode to ground (pin 1) read clockwise on bottom side, which makes almost any radio sound better but not related to hum.