It has rained a ton in the last week... if it goes away when it dries out, I'll let you know. However, the POTS is via FIOS, so there is no copper line outside of the house to be affected, just fiber optic.

I find that if I plug in the computer modem into the POTS line I get the hum as well. I'll try to get a voltage meter and test the lines to find either a short or a ground or something going on. Any suggestions for how to do that?