Does it have the Alpine amp in the rear drivers-side well near the tail-lights? - behind the carpeted panel? You said you looked near the battery... My amp failed ..There was corrosion near the connector and probably a burnt circuit board. Same symptoms. My car is an '05 but had basic stereo..no DSP, No NAV..

The amp I am referring to is a unit by Alpine (in China) Part #65128379376.
You can see several on Ebay to see what I am talking about.