Possible grounding issue - HDMI over CAT-6 electrical arc
Sounds like you may have a hot/ground swap somewhere.  This is very dangerous and could kill somebody if you don't get it figured out.  I would start by checking with a good insulated multimeter to see if we're talking about line-level AC as a first step.  I would also recommend getting one of those outlet grounding testers and check all of the outlets that are involved.  I would also check the ethernet cable runs to make sure that there isn't any damaged insulation or contact with any high voltage wiring.