[Jeffhs]

I cannot for the life of me imagine how just changing the power cord would cause a very loud 60-Hz hum as you are describing; after all, the power cord itself should not have any effect whatsoever on the audio output. If the radio had been working up to now, the only thing I can come up with is a heater-cathode short in one of the audio tubes. Given this radio is very old (pre-WWII vintage), that would not surprise me in the least. Vibration from moving the chassis could have caused such a short, especially if the tube were about to develop an H/K short eventually.

I would not operate the radio in its present condition if it does not have an AC line fuse (it is my understanding that most pre-war radios did not have such a fuse, which all too often led to very serious trouble if a tube were to develop an H/K short or a filter cap would short the same way). The house fuse might blow in case of a shorted tube or filter capacitor, but I wouldn't count on it.