[old_tv_nut]

Random thoughts:

Seems very peculiar that a battery could do that. Could it be some kind of regeneration? Does it only do it with your hand? How about if you place some metal (aluminum foil) near the radio? Does the set have an external ground and/or antenna?

For the HVAC effects, how about snooping around with a transistor portable to see if you can locate the source?

Edit: the source of the buzz could be completely separate from the HVAC, which may be adding its own effects somehow.