Wow. Sure glad that I found this forum. I am having a very similar problem. 2 line AT&T phone (model 992). Separately each line is clean. When I add my VoIP line to the same phone as my POTS line I get hum on the POTS line. This is the second post that mentioned AT&T phone in the problem statement so it could be the root cause. I like the phone isolation solution using a "phone jack extender." Did you put it on the POTS line or the VoIP line. I would guess the VoIP side. I will be going to Radio Shack tomorrow and pick one up.
