Didn't read through all the posts, just the beginning. It seems like OP is experiencing voltage drops from that outlet.
Bear with me (hopefully I didn't miss anything as I didn't read all posts). But having voltage drop too low on an outlet, due to old/poor wiring, will shut off the console, make the wire hot, and display all of the symptoms you are mentioning.
Either voltage drops from outlet, or the power cord has a short, causing "hot spots", which will also cause voltage drops (if it's not due to poor house wiring).
Source: work with car audio high voltage and high powered systems. This is common when you have teenagers thinking you can pull 5k watts on 4 gauge cables, 20 ft from batteries/alternator.