Thank you all for your feedback.  I think we have a plan.
A lighted tester from the hardware store, and a light probe.  It's
funny, because if I use F connectors, no problem, but line audio and hummmmm.
The system is a bit more complex than I discribed earlier.
You see, we have a ten room house with a family that loves TV.
So off this cable line, comes a tv in the kitchen, a
tv/dvd/vcr/x-box/lazor player system in the living room,
a tv/dvd/vcr system in the bedroom, a tv/vcr/play station in another
bedroom, and last of all, a
tv/vcr/dvd/computer/turntable/turntable/cd player/audio cassette
player/open reel tape recorder system in the shack.
So, the only way now to eliminate the hummmm is to disconnect the
cable.  Have tried grounding the cable, and individual chassis, with
minor increases or decreases in hummmm.
Anyway, besides that, many of the outlets are two conductor wiring.
I have been wanting to check outlet polarity for years, and this is a
good excuse.  I might try my radio shack VOM, but the probe that
makes it talk, is loosing it's ability to spring back when you press
the button.

Maybe we have to much stuff around here?