Thanks for all the replies.
New ground rods going in this weekend (weather permitting). Brother will be driving, I will be wiring.
Will try turning off all breakers, except the one feeding the wall outlets, to see what happens, this weekend.
Furnace (new 2 years ago) sheet metal & ductwork to ground checked, no voltage, either to ground or incoming water pipe. (Will check again after new ground rods put in).
Overhead lights to be rewired, separate circuit, with grounds. They are CFL's.(will be replaced with incandescent).
Ceiling tiles are T & G fiber, nailed in place, (no suspended grid), but will be torn down, as brother hates the look. Will be replaced with same style after rewiring.
Have not personally checked bare speaker buzz, but suspect it is as Michael Terrill proposed, the speaker cone is focusing ambient 60 Hz, and when you stick your ear near it, you hear it.
Question concerning water pipe ground. Breaker box is in NW corner of basement. Incoming water pipe is in NE corner, near last wall outlet in the line. Have not checked if any other grounds to plumbing exist. Should this be grounded to the breaker box, with it's own ground wire?
More updates after this weekend.