just had this same problem with my 500e
Turned out to be the cd player. I used a multimeter in-line with the negative battery cable. As soon as I would complete the connection, I would read about 3.5 for the first 10 seconds or so. Then it would drop down to the normal range of .012 or so. When my cd player was plugged in, the reading would never drop past 2.6, so I knew this is where the problem was. Turned out to be a cd jammed in the changer that wouldn't let the unit turn off.